I'll see what I can contribute to this, however I haven't finished my coffee yet so bear with me! If I understand correctly your business aims to conduct both fix and flips and buy and holds. You want to basically develop a "parent" company to manage both of these divisions, or separate LLCs. Your parent company (Company A for arguments sake) would hold your owner contributions. These contributions would be disseminated to "Company B" for flips or "Company C" for buy and holds
-First, let's talk about why you would form an LLC. A real estate business would form an LLC (or other entity) for either tax purposes or asset protection. In your case, it sounds as if you are developing your LLC for asset protection. IE...a rental goes bad resulting in a law suit and you are protected personally from some liability. You should understand from the beginning that each LLC should have a separate bank account and books in order to prevent "piercing the veil" or mixing business with personal. This would surely result in the nullification of your LLC protections should you ever end up in court.
-I'm not sure if you have already started your business or hold any properties currently. Your build out seems like a good idea albeit slightly complicated if you're only holding/flipping a few properties in the first couple of years. Transferring money between completely separate LLCs might cause you some headache in the beginning and not really benefit you how you want it to. If you don't have many properties, I might suggest that you form one LLC to conduct all of your business and branch out into different "divisions" or LLCs at a later time. You may find that your buy and holds a far more profitable and you discontinue your flip business. You could simply stop flipping houses instead of going through the process of closing an LLC.
-To answer a few of your questions specifically, your rent, property management, rental maintenance, etc would all be conducted through your LLC that holds your rentals. All of these transactions would be recorded on that LLC's books and ledgers. All liens, mortgages, etc are held against this company as it will be the company that the property is titled through. I would caution you against titling the property in your parent company then collecting rent, etc through the buy and hold company. This places both companies liable should you find yourself in legal trouble. You should not "siphon" funds between companies. There is a proper way to transfer funds and you should consult your CPA on the proper method. (When I take distributions from my LLC to my personal account, I write an official company check that is recorded in my ledger)
Hopefully this was helpful. Possibly a little scatterbrained. Let me know if I can help any further!
Ben