While our group was in the process of switching from PTA to PTO, we had two bank accounts. We wrote checks from the PTA account and deposited fundraiser revenue to the PTO account. Once the PTA account was down to under $500, we closed the account and deposited to the PTO account. Hope this helps!
Yes, I don't think that would be a problem -- the issue would be if the organization you were donating to was a 501c4, because donations to 501c4s aren't tax deductible. But schools are considered 501c3. (This is also why you should get a 501c3 for your new group.) Best wishes with the process -- I hope it goes smoothly for you.
IRS rules allow one 501c3 organization to donate money to another. That means you can donate money to the school. If you file for 501c3 for your PTO, you may be able to donate the money to the PTO, but that's a bit of a gray area. 501c3 status is retroactive to your start date, as long as you apply for it within 27 months of your start date. So can you donate the money to the PTO, knowing that it will be a 501c3 retroactively? We haven't been able to get a definitive ruling from the IRS on that specific situation.