1. I'm sure there are different contracts for selling shareware to retail customers and for individual programmer selling their software to corporations. Ie look for the 2nd

2. By engaging them on legal terms "Ie I am happy to concede this point but not the other", you already lost since you simply don't know how these things work.

My advice would be to find a standard template and use that - don't try to negotiation with lawyers on legal ground (how likely do you think these lawyers would be better than you at writing code? :)