Sync problems

Well when I read your problem I realized that my Google calendar had not been synced since 6/3 so started doing some research and it seams to be a common problem the one answer that worked for me was to go to settings>manage applications>select show all then find calendar storage then select clear data. This will clear all your calendars data including the phones internal calendar. Once I did this all my events from my Google calendar started syncing again. Not sure if this is a temporary fix but it's working so far. Make sure if you have events on the phones internal calendar that you jot them down because they will be cleared after the data wipe and won't come back. Hope this helps.

8-7-11
To correct your other problems I would delete your gmail account from the phone turn the phone off and then back on and then create again.