Re: GA - are you living/operating outside of Georgia? You may have to register to do business in other states depending on your activity outside the state of organization.
Re: the LLC - why’d you organize as an LLC (not saying it was an incorrect decision; it was probably a good decision, just would be helpful to see your reasoning so people can better provide advice to meet those goals). Also, how many members, and have you made any election to be taxed as a corporation?
1 - Depends on where you’re operating and what you need from the bank. If you’re just looking for a personal checking account style (conducting personal-like transactions) that just has your entity name on it, check with local credit unions and the usual suspects in your area (Chase, etc). If looking for something specific for business accounts (positive pay, payroll handling, check handling, etc.) I’d recommend probably sticking to the big players or certain high service level banks (First Republic, City National, etc.)
3 - Depends what you need from it. You can create an invoice in word/pdf/excel for free. As for payroll, if you are the sole member of the LLC and the LLC is taxed under the default rules, you aren’t an employee, you would make distributions from the LLC to you pursuant to the operating agreement and state law.
4 - My biggest piece of tax advice is: don’t waste money to get deductions.
5 - Don’t be afraid to hire one or multiple people if the work demands it, have a process in place for collecting money and one in place for what happens if you aren’t able to collect, absolutely talk to a lawyer (hopefully talked to one when you setup the LLC as well) if you’re changing the membership in the LLC,