Emails are only being delivered to the WebOutlook inbox and not my desktop outlook

Question

1.  Big Problem:  How do I get emails sent to my primary email address (name @ wealthblush dot com hosted by Go Daddy) to go to both the
Outlook Web App inbox AND the inbox of my desktop Outlook 2013? They only go to
Outlook Web App and not my desktop Outlook 2013.
How is the email account configured in Outlook (POP3, IMAP or Exchange):
POP/SMTP is for the user @ wealthblush dot com - this is the one where the email ONLY goes to the Outlook Web App, but not into Desktop Outlook 2013.
IMAP/SMTP  is for the user @ charter dot net email. Emails go to both clients, but if I delete on one client it is not deleted on the other.
Exchange/ActiveSync is the outlook.com email and it only goes to my desktop Outlook.
I'm not getting any error messages. Mail is being delivered to the user @ wealthblush dot com, but only to Outlook Web App and NOT my desktop Outlook.
2.  How can I change the inbox an email account puts incoming emails into? I read somewhere the way to do this is to create a search folder? This question is actually in advance of fixing
question number 1 above.
3.   I don't know how I should configure my emails with the new Outlook 2013 now being in the cloud:
    - I have an @ outlook dot com email I setup when MS came out with the free outlook dot com (hotmail), but I never used it because the reminders didn't work the same as in desktop outlook (not being able to snooze for a few hours
or days or weeks if I remember right and the way we get the alerts too).
    - I also have an email with my ISP (@ charter dot net) which is a mix of personal and business emails. I've had this account for over 10 years.
    - Finally, I have a business website (www dot wealthblush dot com) hosted by GoDaddy with one real email @ wealthblush dot com. I've already setup the aliases for several other emails in my new office 365 account (support,
sales, webmaster at wealthblush dot com) which are configured to pass into specific folders using Outlook 2013 Rules in my desktop outlook. I'm not sure if those rules are replicated into the office 365 account.
I still want the aliases to go into those folders like before.
4.  In the case of my outlook.com email, they do go to both inboxes (on the web and desktop), but when I delete an email from one place, shouldn't it get deleted in the other place as well? How do I get them to synch?
5.   And then there's my existing .pst files. I have 4 of them with old emails I've saved over the years that takes up just over one GB. I save these .pst files to DVD everyday so I can go back to look at something if I need to (and for hard drive
crashes). Does MS want me to import all that stuff to their servers and get rid of my .pst files? Does MS want me to put everything into one .pst file? It seems like it? If I do then I assume things need to be synchronized all the time between my file and
your .pst file? The synchronization process is as close as you can get to real-time, right? Or does each individual change get sent as it happens?
6.  I also have a skydrive account from a while ago too. Is this where I should put my documents so they're accessible when I'm not at my desk? Now, that would be a LOT of data (probably close to 80 GB). Or, is the intention for us users
to only put certain current docs in this area. I assume these files can be synced with my desktop too, right? But I don't know how to. Do you keep old versions of the files in skydrive so we can recover them? I want to know if I can use your service to hold
my files (they would ONLY exist on your system and you'll back them up and I can get old versions back when needed).
7.  Is an option to keep everything on my desktop 2013 like I did in 2010 of Outlook, bypassing the cloud and MS mail servers all together?
Sorry about all the questions, but I'm just getting the feel for your approach and need to decide how this all should fit together, do it, then go back to my business. I'm by myself at my company right now, but I'm planning on hiring a few people
real soon too so I need to keep this in mind. I've worked with Outlook since it came out, and I've configured it, but mainly only for myself and my family.

Answer 1

R1: Seems you didn't configure you email account in your Outlook client properly. please refer to the following KB article and try to create a new mail profile to configure your email account again:
http://support.microsoft.com/kb/2758902
R2: Do you want create subfolders under Inbox to category your emails? If so, we can just right click on Inbox > select New Folder... After that, we need to create rules to move or copy your emails to each subfoler. See:
http://office.microsoft.com/en-us/outlook-help/manage-email-messages-by-using-rules-HA010355682.aspx
Besides, in order to avoid confusion and keep track of troubleshooting steps, we usually troubleshoot one issue per thread in order to find a resolution efficiently. Concerning your other question, I suggest we create new posts for your other questions via:
http://social.technet.microsoft.com/Forums/en-US/home?forum=outlook
Thanks for the understanding.
Steve Fan
TechNet Community Support