I offered $52k and seller accepted, multiple contracts fell through already, I was told.

Take the Agent for a test Drive - meaning go out with the Agent to see how you mesh personality wise.

Payoff is more than the house is worth, so had to negotiate with them to get them to accept less.

I found the preforclosure list and tax delinquency list in my county and have been studying them fora couple days now.So today while coming back from going out with the family I decided to test my tax delinquency list to confirm or deny my assumptions by driving pass a house on my tax list and sure enough, it looked abandon and showed all the signs I've read about and I heard.

I found the preforclosure list and tax delinquency list in my county and have been studying them fora couple days now.So today while coming back from going out with the family I decided to test my tax delinquency list to confirm or deny my assumptions by driving pass a house on my tax list and sure enough, it looked abandon and showed all the signs I've read about and I heard.

Should I avoid lowering out of that range to encourage acceptance of my terms?

Accepted the request. 

Let him know that it is not acceptable to do this very often though. 

You can test your skill by just looking at the MLS in that area.

No personal story , makes you seem desperate, stick to the facts that you have money and you can pay x amount of dollars and ready to proceed with purchase if offer accepted!