Default Gateway when connected to VPN

Question

Thanks for reading!
This is probably a dump question so bear with me...
I have set up a VPN connection with a Cisco ASA 5505 fronting internet, with the customers environment behind it (on the same subnet), When connected ot the VPN I can reach the inside Router fronting me and one switch behind the Router (every switch is connected to the router), but nothing else.
My beet is that the Router is messing with my connection, but,, nevermind that!, the setup ain't complete anyway... my question is more related to the Gateway I'm missing when I'm, from the outside, is connected to the VPN on the ASA, could this mess it up? Shouldn't I have a Standard-Gateway in the ipconfig settings in windows?
This is who it looks like now:
        Anslutningsspecifika DNS-suffix . : VPNOFFICE
        IP-adress . . . . . . . . . . . . : 10.10.10.1
        Nätmask . . . . . . . . . . . . . : 255.255.255.0
        Standard-gateway  . . . . . . . . :
The internal network is :
172.16.12.0 255.255.255.0
Below is my config for the ASA, thanks a lot!!!!!!!
!FlASH PÅ ROUTERN FRÅN BÖRJAN
!asa841-k8.bin
hostname DRAKENSBERG
domain-name default.domain.invalid
enable password XXXXXXX
names
interface Vlan1
nameif inside
security-level 100
ip address 172.16.12.4 255.255.255.0
interface Vlan10
nameif outside
security-level 0
ip address 97.XX.XX.20 255.255.255.248
interface Ethernet0/0
switchport access vlan 10
interface Ethernet0/1
interface Ethernet0/2
interface Ethernet0/3
interface Ethernet0/4
interface Ethernet0/5
interface Ethernet0/6
interface Ethernet0/7
ftp mode passive
clock timezone CEST 1
clock summer-time CEDT recurring last Sun Mar 2:00 last Sun Oct 3:00
dns server-group DefaultDNS
domain-name default.domain.invalid
object-group protocol TCPUDP
protocol-object udp
protocol-object tcp
access-list nonat extended permit ip 172.16.12.0 255.255.255.0 10.10.10.0 255.255.255.0
access-list MSS_EXCEEDED_ACL extended permit tcp any any
access-list VPN-SPLIT-TUNNEL remark VPN SPLIT TUNNEL
access-list VPN-SPLIT-TUNNEL standard permit 172.16.12.0 255.255.255.0
tcp-map MSS-MAP
  exceed-mss allow
pager lines 24
logging enable
logging timestamp
logging buffer-size 8192
logging console notifications
logging buffered notifications
logging asdm notifications
mtu inside 1500
mtu outside 1500
ip local pool VPN 10.10.10.1-10.10.10.40 mask 255.255.255.0
icmp unreachable rate-limit 1 burst-size 1
icmp permit any inside
icmp permit any outside
asdm image disk0:/asdm-625-53.bin
no asdm history enable
arp timeout 14400
global (outside) 1 interface
nat (inside) 0 access-list nonat
nat (inside) 1 172.16.12.0 255.255.255.0
route outside 0.0.0.0 0.0.0.0 97.XX.XX.17 1
timeout xlate 3:00:00
timeout conn 1:00:00 half-closed 0:10:00 udp 0:02:00 icmp 0:00:02
timeout sunrpc 0:10:00 h323 0:05:00 h225 1:00:00 mgcp 0:05:00 mgcp-pat 0:05:00
timeout sip 0:30:00 sip_media 0:02:00 sip-invite 0:03:00 sip-disconnect 0:02:00
timeout uauth 0:05:00 absolute
dynamic-access-policy-record DfltAccessPolicy
aaa authentication ssh console LOCAL
http server enable
http 172.16.12.0 255.255.255.0 inside
no snmp-server location
no snmp-server contact
snmp-server enable traps snmp authentication linkup linkdown coldstart
crypto ipsec transform-set ESP-AES-256-MD5 esp-aes-256 esp-md5-hmac
crypto ipsec transform-set ESP-DES-SHA esp-des esp-sha-hmac
crypto ipsec transform-set ESP-DES-MD5 esp-des esp-md5-hmac
crypto ipsec transform-set ESP-AES-192-MD5 esp-aes-192 esp-md5-hmac
crypto ipsec transform-set ESP-3DES-MD5 esp-3des esp-md5-hmac
crypto ipsec transform-set ESP-AES-256-SHA esp-aes-256 esp-sha-hmac
crypto ipsec transform-set ESP-AES-128-SHA esp-aes esp-sha-hmac
crypto ipsec transform-set ESP-AES-192-SHA esp-aes-192 esp-sha-hmac
crypto ipsec transform-set ESP-AES-128-MD5 esp-aes esp-md5-hmac
crypto ipsec transform-set ESP-3DES-SHA esp-3des esp-sha-hmac
crypto dynamic-map SYSTEM_DEFAULT_CRYPTO_MAP 65535 set pfs group1
crypto dynamic-map SYSTEM_DEFAULT_CRYPTO_MAP 65535 set transform-set ESP-AES-128-SHA ESP-AES-128-MD5 ESP-AES-192-SHA ESP-AES-192-MD5 ESP-AES-256-SHA ESP-AES-256-MD5 ESP-3DES-SHA ESP-3DES-MD5 ESP-DES-SHA ESP-DES-MD5
crypto map outside_map 65535 ipsec-isakmp dynamic SYSTEM_DEFAULT_CRYPTO_MAP
crypto map outside_map interface outside
crypto isakmp enable outside
crypto isakmp policy 10
authentication pre-share
encryption 3des
hash sha
group 2
lifetime 86400
crypto isakmp policy 65535
authentication pre-share
encryption 3des
hash sha
group 2
lifetime 86400
telnet timeout 5
ssh 172.16.12.0 255.255.255.0 inside
ssh timeout 5
console timeout 0
threat-detection basic-threat
threat-detection statistics access-list
group-policy VPNOFFICE internal
group-policy VPNOFFICE attributes
dns-server value 215.122.145.18
vpn-tunnel-protocol IPSec
split-tunnel-policy tunnelspecified
split-tunnel-network-list value VPN-SPLIT-TUNNEL
default-domain value VPNOFFICE
split-dns value 215.122.145.18
msie-proxy method no-proxy
username admin password XXXXXX privilege 15
username Daniel password XXXXX privilege 0
username Daniel attributes
vpn-group-policy VPNOFFICE
tunnel-group VPNOFFICE type remote-access
tunnel-group VPNOFFICE general-attributes
address-pool VPN
default-group-policy VPNOFFICE
tunnel-group VPNOFFICE ipsec-attributes
pre-shared-key XXXXXXXXXX
class-map MSS_EXCEEDED_MAP
match access-list MSS_EXCEEDED_ACL
class-map inspection_default
match default-inspection-traffic
policy-map type inspect dns preset_dns_map
parameters
  message-length maximum 512
policy-map global_policy
class inspection_default
  inspect dns preset_dns_map
  inspect ftp
  inspect h323 h225
  inspect h323 ras
  inspect netbios
  inspect rsh
  inspect rtsp
  inspect skinny 
  inspect esmtp
  inspect sqlnet
  inspect sunrpc
  inspect tftp
  inspect sip 
  inspect xdmcp
  inspect icmp error
  inspect pptp
  inspect ipsec-pass-thru
  inspect icmp
class MSS_EXCEEDED_MAP
  set connection advanced-options MSS-MAP
service-policy global_policy global
privilege cmd level 3 mode exec command perfmon
privilege cmd level 3 mode exec command ping
privilege cmd level 3 mode exec command who
privilege cmd level 3 mode exec command logging
privilege cmd level 3 mode exec command failover
privilege cmd level 3 mode exec command packet-tracer
privilege show level 5 mode exec command import
privilege show level 5 mode exec command running-config
privilege show level 3 mode exec command reload
privilege show level 3 mode exec command mode
privilege show level 3 mode exec command firewall
privilege show level 3 mode exec command asp
privilege show level 3 mode exec command cpu
privilege show level 3 mode exec command interface
privilege show level 3 mode exec command clock
privilege show level 3 mode exec command dns-hosts
privilege show level 3 mode exec command access-list
privilege show level 3 mode exec command logging
privilege show level 3 mode exec command vlan
privilege show level 3 mode exec command ip
privilege show level 3 mode exec command ipv6
privilege show level 3 mode exec command failover
privilege show level 3 mode exec command asdm
privilege show level 3 mode exec command arp
privilege show level 3 mode exec command route
privilege show level 3 mode exec command ospf
privilege show level 3 mode exec command aaa-server
privilege show level 3 mode exec command aaa
privilege show level 3 mode exec command eigrp
privilege show level 3 mode exec command crypto
privilege show level 3 mode exec command vpn-sessiondb
privilege show level 3 mode exec command ssh
privilege show level 3 mode exec command dhcpd
privilege show level 3 mode exec command vpnclient
privilege show level 3 mode exec command vpn
privilege show level 3 mode exec command blocks
privilege show level 3 mode exec command wccp
privilege show level 3 mode exec command webvpn
privilege show level 3 mode exec command module
privilege show level 3 mode exec command uauth
privilege show level 3 mode exec command compression
privilege show level 3 mode configure command interface
privilege show level 3 mode configure command clock
privilege show level 3 mode configure command access-list
privilege show level 3 mode configure command logging
privilege show level 3 mode configure command ip
privilege show level 3 mode configure command failover
privilege show level 5 mode configure command asdm
privilege show level 3 mode configure command arp
privilege show level 3 mode configure command route
privilege show level 3 mode configure command aaa-server
privilege show level 3 mode configure command aaa
privilege show level 3 mode configure command crypto
privilege show level 3 mode configure command ssh
privilege show level 3 mode configure command dhcpd
privilege show level 5 mode configure command privilege
privilege clear level 3 mode exec command dns-hosts
privilege clear level 3 mode exec command logging
privilege clear level 3 mode exec command arp
privilege clear level 3 mode exec command aaa-server
privilege clear level 3 mode exec command crypto
privilege cmd level 3 mode configure command failover
privilege clear level 3 mode configure command logging
privilege clear level 3 mode configure command arp
privilege clear level 3 mode configure command crypto
privilege clear level 3 mode configure command aaa-server
prompt hostname context
Cryptochecksum:aaa1f198bf3fbf223719e7920273dc2e
: end

Answer 1

I didn't realise I had that crypto settings on, thanks my bad!!!
But... the 172.16.12.0 network is directly connected, the Router (that to be honest is a firewall) / switches is all on the same subnet (172.16.12.X/24), so sorry I didn't explain thoroughly, was more wondering about the GW and didn't want to overcomplicate things..
The Firewall/Router dosen't do any routing, so it should work right (I you count out the firewalling in the firewall and so forth, there shouldn't be any problems accomplishing this with the ASA)? The Firewall is more a DHCP for the clients/Firwall for the clients.. this will change in the future.. it will be removed,
the vpn network is staticly routed back to my ASA in that firewall...
I don't like this solution.. but this is who it looks.. for now..
(VPN network is 10.10.10.X/24)
But... shouldn't I see a default gateway under ipconfig when I'm connected to the VPN from internet, on the vpn client that's vpned in, is this correct?
THANKS for all the help!