@Jahan Habib The rule of thumb in the financial world, that I've observed, is that when you're offering to move a good amount of $ to a company, they are eager to help you do so as quickly as possible.
On the other hand, depending on where you currently have the money, that company may drag its feet on the rollover/transfer - when you're moving a good amount of $ out of a company, their incentive is to give you as little help as possible (not to mention charging some kind of exit fee in many cases).
To be safe, mainly because of the latter (feet dragging from the company losing your business), I would estimate it could take up to a month.
Yes, it is possible for your IRA-controlled LLC to receive financing, but my understanding is that true non-recourse financing is still a little challenging to find, that there are only a handful of companies doing it.
As far as fees, "everything's negotiable" - be sure to ask for estimated fees up front. It's possible there will be a mortgage origination fee, an application fee, an appraisal fee, mortgage points, mortgage doc prep fees, lender's title insurance fees, recording fees, and other miscellaneous fees.
It's possible there could be a credit check fee on you personally BUT there honestly should not be such a fee because you cannot personally guarantee the loan, so in my opinion they should have no business checking your credit on a non-recourse loan. If they insist, I would make it clear, absolutely, 100% crystal no-misunderstanding clear, that you will NOT sign any personal guarantee on the loan under any circumstances, and if you get to the closing table and they stick one in front of you and tell you sign it or you lose the deal/deposit, you will walk away from that closing table.
The reason I say this is that a number of SDIRA owners in the past have had exactly that happen, they thought it was non-recourse and then at the closing table were asked to sign a personal guarantee, and some of them did.
BAM - that counts as "extending credit" to your IRA, which is a prohibited transaction, and my understanding is the IRS considers your whole IRA distributed at that point - and then proceeds to assess penalties and taxes accordingly.
There are 1000 different ways to shoot yourself in the foot with SD IRAs, they are powerful but very tricky to get right, and the penalty for making a mistake can potentially be a lot of your retirement savings. You really need to pick a good custodian and do exactly what they tell you, don't try to hide things from the custodian or think you're going to skirt around the SD IRA rules.
If you have questions, direct them to your custodian. For example, the custodian can tell you whether FHA/HUD loans are non-recourse (I honestly don't think they are non-recourse), and possibly provide you a list of lenders their clients have worked with, who they know are bona fide non-recourse lenders.
(They probably won't "recommend" any companies, but you might get a list of "here are some companies our clients have used in the past, which we believe offer true non-recourse loan programs; as with all investments you are responsible for doing your own due diligence on the lender, the property and the deal")
I hope this helps!