I wish to get our own title search done as I don't trust theirs .I don't want to send the emd in fear of losing it if title has issues.  

But now it's the first listing on google search and I'm losing a lot of business b/c of this.

You'll lose the deal.The deal is, a couple coats of new paint over lead based paint is how you fix it.  

If I go ahead with the first applicant, I lose nearly $1000 in rent for the April 1 to 12 period.2) If I reject the first applicant for this reason, am I expected to reimburse them for the credit and background checks?

Other wise you'll lose your EMD.  

I break in plenty (if a window is open or something).Selling its worth losing some appliances once every 10 years versus driving to a house to show every Looky Lou that comes around.Maybe you're in rougher areas than I work, but I have way more trouble with contractors stealing from me than I ever have with buyers.

Then again I only buy single family homes from people who are going to lose them to the bank anyway.I agree with @Dion DePaoli to go with an installment sale.

Go with your gut - if your gut tells you something's off, it's far better to lose a sale...

I've picked up several of these deals & closed them over the last few months.One could not be closed, and they faced the choice of a HML or losing their EMD

If you have an apartment building and the Hells Angels moves into one of your units, you need to move them out or risk losing your good tenants.