@Josh Boyd LLC functions vary by state. I can answer your question according to Arizona procedures, which might be illustrative to you but are in no way exactly what you can or should do in Georgia.
1) Your LLC doesn't have to purchase your house. You can contribute it as a business asset by deeding it to the LLC. I know that in some states this triggers a stamp tax or some other transaction cost. In Arizona, the deed recording is $15 or so + the cost of someone writing up the deed if you choose to engage someone to do that. You've contributed the asset to the LLC no different than if you capitalized it with cash.
2) See above. Your LLC doesn't have to put anything down. BUT, there will likely be a discussion of the validity of your existing mortgage as it relates to the LLC. There are two considerations: 1) due on sale clause, and 2) piercing the corporate veil. #1 has been mitigated in many cases since Fannie Mae allows their the property securing their loans to be transferred into a Single-Member LLC. You may or may not have a Fannie Mae loan, and your original lender may or may not permit this to happen without triggering the due on sale clause. But Fannie Mae's decision makes it a more widely-accepted practice. Check your own situation to the extent that it gives you comfort. #2 generates a lot of discussion. I've yet to see someone cite a case in which the corporate veil of an LLC has been pierced solely because the mortgage was originally written to the person and not the LLC, but theoretically it's possible. Running your operation like a true arm's-length business with it's own accounts and accounting procedures, not co-mingling funds, taking proper draws when you need funds to pay personal expenses (as opposed to writing a check from the business account), all strengthen the separation between you and your LLC. As for the mortgage, I can't provide any cases where this has been argued, but I argue that many of my non-real estate business debts (credit cards, lines of credit with personal guarantees, etc) are as much based on my personal credit and are personal liabilities as the mortgage that was also secured personally...and is now deemed permissible by Fannie Mae. That's my view and the view of the counsel I've sought. You need to seek your own.
3) Not sure exactly what you are trying to do (pull the 229?), but if you need cash, you might consider securing a line of credit on the house while it's still your primary residence. That will be a LOT easier than after it's become non-owner occupied, and especially if it's non-owner occupied in an LLC. It seems to me that the lender's recourse if they don't like your having converted it to a rental after closing the LOC, is to pull the line. Oh well. You might be charged an early-closure fee, but that's all. My feeling is that they'll do nothing and not care so long as the line is being paid. But you have to decide what you want to do.
4) The answer to #2 was no, so this is moot.
Again, that's all perspective from my experiences in Arizona. LLCs are are state law entities, and courts in each state may handle them differently. As always, check with local counsel for important questions.
Good luck!