I am already amazed at the ideas some people come up with here. Basically, from my perspective, the seller has the advantage and initially sets the conditions. If there are multiple interested parties, your room for negotiation is rather limited. Then either accept or keep looking.
We will soon be in a similar situation and will certainly not accept excessive rental demands and the like. The real estate market is still a seller's market; it should be fair and understandable for both sides. I have no regard for any restrictive conditions, and even such proposals would make me consider looking for another buyer / awarding the contract elsewhere.