Updated to mavericks now multiple problems. mainly mail

Question

I updated to osx 10.9.1 and am using safari 7.0.1   now having multiple problems.  It may take up to 8 hours to get our Gmails on mail.  if we are typing an email, we may take say 10 min typing the email.  We can then go to our mail trash and there might be 15 to 20 deleated versions of that email in difrernt stages of completations we were typing.  Also can delete trash and junk and they might go away or at times they will come back with 1,2, or may be 3 sets of the emails that we deleated.  looked at all the settings I could find to see if something is set wrong but not finding anything.  Verry frustrated.  Tried to open the download osx10.9.1 update bur would get an alert that " this software is not supported on your system".  I need help

Answer 1

Fixing a Mavericks Installation Problem
How to manage a failed OS X Mavericks installation | MacFixIt - CNET Reviews.
Try these in order:
1. a. Resetting your Mac's PRAM and NVRAM
    b. Intel-based Macs: Resetting the System Management Controller (SMC)
2. Restart the computer in Safe Mode, then restart again, normally. If this doesn't help, then:
     Boot to the Recovery HD: Restart the computer and after the chime press and hold down the
     COMMAND and R keys until the Utilities menu screen appears. Alternatively, restart the computer and
     after the chime press and hold down the OPTION key until the boot manager screen appears.
     Select the Recovery HD and click on the downward pointing arrow button.
3. Repair the Hard Drive and Permissions: Upon startup select Disk Utility from the Utilities menu. Repair the Hard Drive and Permissions as follows.
When the recovery menu appears select Disk Utility. After DU loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list.  In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive.  If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit DU and return to the main menu. Select Restart from the Apple menu.
4. Reinstall Lion/Mountain Lion, Mavericks: Reboot from the Recovery HD. Select Reinstall Lion/Mountain Lion, Mavericks from the Utilities menu, and click on the Continue button.
Note: You will need an active Internet connection. I suggest using Ethernet if possible because it is three times faster than wireless.