Jorge,
Congrats on getting started. Some thoughts on your questions below (context: I am a partner in a hard money lending business).
1. Let's first make the distinction between hard money lending and private lending. Hard money is a loan on the underlying asset. Most HML's are going to only be able to loan to LLC's or corps due to the Dodd-Frank legislation requirements on consumer loans. Private money can come from any individual, typically friends and family when you are getting started. Private money could be unsecured by the asset (i.e. you could borrow the money from your mom or grandpa, best friend, etc.) in the form of a promissory note, or it could be tied to the property itself with a deed of trust or mortgage. Private money can be loaned to an individual or an LLC/Corp, but keep Dodd-Frank in mind.
2. Conventional 30 years financing is most commonly issued to individuals, not LLC's. If you quit claim the property from your LLC to yourself, it may be a taxable event - so be sure to consult your tax pro before doing anything. Also be aware that the original lender (hard money or private) will likely not be a fan of you using a quit claim while you have a loan out (in my business, we do not allow this). They likely will have language in your loan docs that specifies what the consequences could be if transferring the title to another entity or yourself while the original loan is still outstanding. You could have the loan called due. Private money lenders (especially friends/family) may be more flexible on this stance than a HML.
3. This is going to vary widely from lender to lender. As I mentioned above, friends and family are common private money sources and will likely be more flexible with terms than an institutional lender. The easiest way to do what you are describing is to use an LLC to buy the property, finish your rehab, then refinance out of the hard money loan into a commercial loan using the same LLC with a commercial lender (or private lender if you have access to one). Pros - A lot less paperwork and headaches with commercial loans vs conventional loans, plus faster decisions and processing times. Cons - typically shorter amortization period, higher interest rates, and shorter periods of fixed interest before ballooning.
Hope some of this helps. Feel free to DM me if any questions.
Good luck!
Owen