If you are dealing with a commercial lender, the most likely scenario is that if you continue making payments, the lender won't care about the transfer, even if they do have a technical right to call the loan. And some due on sale clauses permit the type of transfer you described. If you are concerned, have a real estate attorney look over the documents for a more definite answer.
As for the insurance - you should have adequate insurance coverage whether the property is owned by you or by an LLC. Just from a post on this web site, there is no way to really advise you on what would be adequate and who needs to be named in the policy or policies.
This answer is for general purposes only, and it does not create an attorney-client relationship.
I don't know about Georgia law, but typically mortgages will include due-on-sale clauses that might require the full value of the mortgage to be paid upon transfer. You should consult with an attorney and have them look over your paper work before doing anything on your own, since you wouldn't want the bank to call your loan simply because of the transfer. Usually an attorney would write the bank a letter asking for permission to transfer to an LLC.