Gmail fetch problem and something else

Hi,

I have set up on my iphone ver 2.2 the gmail imap acount through the iphone.

Fetch is set to 30 mins, i've disabled push bcz gmail does not support push anyway (apart from android so they say) and to reduce battery use.

Two issues I can't seem to solve:

My phone does not fetch while in sleep, if I dont touch it for more than 30 mins, I open it and it shows last updated in a time more than 30 mins. sometimes even 2 hours and no fetching.

Other thing - that may be the cause: when i wake up the phone from sleep - unlocking it, and going to the gmail and pressing update manually (due to the problem i described before) the iphone cant connect to the wifi on first time and gives me msg regarding unable to connect to 3G (I've disabled that throgh the iphone option and through my cellular company - I dont have a data plan).
After getting those cant connect to 3G msg's i press again and then it connects and download the emails - if there are new ones.

I have a wireless router that i configured with my iphone - safari doesn't seem to have problem connecting from sleep right away.

Any suggestions?

Thanks,

Nitay