@Tim Hawkins Talk to a lawyer :) though my wife and I did the same in recent past and this is what we learned. (and everything Steve V. mentioned above it true and accurate; hopefully my answers will help to clarify)
1. With my name being the only one on the LLC paperwork but all the loan and banking being in both our names, should my wife be listed as a registered agent as well?
Being the RA doesn't convey any ownership or the LLC. It only indicates the primary contact for the LLC (since some LLCs are created anonymously). In fact, I believe there is only a single RA on any LLC.
You might mean that you want to put her as a Member (Owner) of the LLC (which is different than the RA). Steve's answer is correct about how the LLC might treat spouses who each own half of an LLC.
What we did was put our family trust as the sole member of the LLC, thus it is a single entity LLC (thus a disregarded LLC), and both my wife and I are the trustees of the family trust, so we share ownership. We it all eventually flows onto our joint Schedule E. Whew!
2. If so, regarding the IRS, would that then make the LLC more than a single member LLC, and would we still be able to be considered a disregarded entity?
See previous comment.
3. Since there are no "employees" in the LLC, my understanding is that no EIN in needed, only a TIN, which would be my/our SS#'s. Is this correct?
We have an EIN for our disregarded LLC.
4. I am looking at opening up a business account in the LLC's name, the bank says I need an EIN, but the IRS says I only need a TIN (my SS#) since there are no employees.
We use the LLC's EIN and avoid using our SS#s.
5. Lastly, if the loans are in our personal names but everything else is done/moved under the LLC
name, do I need to look at refinancing the property under/into the LLC,
or is it still beneficial to have the LLC with the loans under our
personal names?
We have kept our loan in our personal name, and the bank is good with that. They knew it was an investment purchase. The details of what we did are: we actually put the property into a land trust which avoids the loan-call and avoids property transfer taxes. And our LLC is the beneficiary of the land trust (which has the family trust as the beneficiary). Took me a while to understand this structure, but we are good to add more properties via individual land trusts which will have the LLC as the beneficiary. Whew!
6. Have I unnecessarily over-complicated things for a single rental by LLC'ing?
Yes. We did too. But we are planning to add more properties to our holdings in the coming year, so we're set for growth.