Accepting buyer's offer with conditions?

You could ask for a mortgage non-contingency (which would mean the buyer will still be bound even if his bank denies financing). Mortgage contingencies have been pretty standard in recent years. But why not just counter with your 'where I want to end up' number? If it's not far off, you'll probably get it.

I wouldn't ask for no mortgage contingency for a buyer who needs a mortgage, I believe it would be a nonstarter for most buyers. I need to confirm with my broker, but there is a good chance the offer is "final and best" to avoid triggering an additional tax (starts with m, lol) at a higher number. But for this, I believe we could settle somewhere 5-10k higher.

I know that buyers will sometimes ask the seller to cover part or all of their closing costs as part of their offer. Do sellers sometimes do something similar? For example, could I counter with his offer price plus he pays certain of my fees (e.g., attorney fees)? If so, which fees would get me to 5-10k more?

That would be your 1.825% transfer tax for properties above 500k