GoPhone plan switching back and forth between $2 a day and $40 a month plans

Monthly plans are 30 days, no proration on plans is possible.  I don't know much about the $2 per day plan, but you are charged only when you use the phone.  

https://www.att.com/shop/wireless/gophone-plans.html

Changing rate plan. https://www.att.com/esupport/article.html#!/wireless/KM1040985

I also see that on the $40 a month plan, that unused data is rolled over at the end of the month. Would unused data be rolled over to my $2 a day plan if I switched at the end of 30 days.

Nope.   If you change plans you lose the rollover.  That's any change, from any plan.  

when they hop from plan to plan. there's no prorations you loose the month that you paid for so it's best to wait and get your moneys worth.. because you will loose it.. when i went from the 30.00 a month plan to the 45.00 i lost what was left of the 30.00 a month plan. i waited so it didn't matter to me!! i don't know if you'll loose your data but knowing go phone or any other pre paid service you'll loose your data

When you plan your strategy to switch out of a monthly plan, is it always exactly 30 days or if you jump in on the 5th of the month, are your charged again on the 5th next month, etc?

It's 30 days.