Agree with Maigahane - MFS can really screw with some of your deductions. You have to look at all the facts to decide which way is better, but 95% of the time MFJ wins out.
Medical expenses - you can only claim your own.
Rental property - The big expenses tend to be mortgage interest and depreciation. The mortgage interest will be reported on a form 1098, which will have a name and social security number (or FEIN) on it. This is really who should be claiming the interest deduction to avoid IRS notices, so this is who should really be claiming all rental income and expenses. I think you have some flexibility, but it would be smart to change the deed and mortgage if your husband were to claim this activity.
You can claim a portion of the mortgage interest, but you might get tax notices from the IRS a year later. They're called CP-2000 notices. They have a system that matches your SSN reported on all forms to what you reported on your 1040. If it turns up different, they send a notice. You then just have to respond to the notice explaining your reasoning, and maybe provide some documentation.
Lending Club - Again, this will be tied to your SSN. Open an account in your Husband's name/SSN if you need him to claim it.
With MFS, you have to both claim itemized deductions, or both claim the standard deductions, you can't do one of each. You can't claim any student loan interest. You lose out on some other things, but it really comes down to all the factors in your return. Chances are, it's not worth your time to split it all up, but you don't know unless you try.