I love airplane buying because it is capitalism at its best. There is a commodity (the plane) and your money. The two parties involved in buying and selling negotiate until the party selling gets hit with enough money to part with the commodity. The party buying doesn't give up his/her money until a commodity is worth the $.
First rule - keep your money as your money till the very last minute. Don't part with a cent until you have the entire package in front of you.
Let's do a used car instead. You go see a car that is of the type you want and has a reasonable "asking" price. You test drive the car and find that the fuel gauge is broken and there is an undefined squeaking noise. The owner says he'll get the fuel gauge fixed and the squeak is just the springs and the car hasn't been driven much. Now what are you going to do? Well you were interested in the car, but you've got three nagging doubts. 1.) Will he get the fuel gauge fixed and in what time frame? 2.) Is the squeak just the springs or something worse? and 3.) If the car hasn't been driven much, what other problems are there?
You can demand an inspection. You can negotiate a lower price. You can wait until the car is fixed to satisfaction. In the last one, you may lose the car to someone less picky.
So. let's go back to the plane. You said its not a popular plane and it seems like you may be the only interested party. Less of a requirement for you to put any kind of "holding" deposit.
The AI and the shimmy damper need to be looked at by your pre-buy professional mechanic. You have no way to assess what is going on with these (PS, new tires do NOT cause a shimmy unless they were installed by a basic moron!) The price is not negotiable right now because you may have to buy a $600 AI and you may have to have the shimmy fixed (which could cost $20 and could cost $600??).
As to the pre-buy - this is often a sticky situation. In the end, the easiest way to do this is to send YOUR mechanic to the field where the airplane is. The mechanic can go over the plane and give you a report. Sometimes this is not practical. Now you have to negotiate the transport of the airplane to the mechanic. Owners have a hard time parting with their birds - so either you have to talk the owner into an X-C with him driving and you paying or you have to give him a deposit and get a ferry pilot to fly the plane to the mechanic. Again - it's your money - try to spend as little of it as you can. And if you do spend the money, make sure you get something for it. For example, you pay a reputable mechanic to go down and inspect the plane. You are at least deriving a service for your dollars. Let's say you give the owner a deposit and he decides he doesn't want to go through with the sale - OK where's your piece of paper (contract) saying that you will be refunded.
Do not negotiate a price until you know all the details about the plane. Right now, you can say something to the owner like his price is reasonable, but...... (the items of the pre-buy inspection). You can say to him that his asking price is already too high and you need the price to be reduced by xxx dollars before you will start negotiating (probably will lose that plane).
Like the used car, though, you are not expecting perfection. This airplane will not be factory new. There will be blemishes and mechanical problems. Some you can accept, some you can't. My pet peaves are corrosion in the airframe and an under-used engine. I can't even stand to look at airplanes that have been sitting on the ground and rusting away. You can give me a 6,000 hr beat up paint job and interior with a worn engine dripping oil, but if the logs indicate that it has flown 20 hours every month since new, I'd be happy as could be. The plane can be repainted, a new interior installed and the engine overhauled. Corrosion, though, is like having cancer. You just don't know.
So, talk with the owner and negotiate how you are going to do the pre-buy. Don't even talk money right now until you have some real input into what the airplane has wrong with it. Be willing to walk away. If the owner won't negotiate or work with you - it may be a warning sign of something he's trying to hide. The commodity is just that. You are buying a hunk of metal. Today, tomorrow, whatever. Remain calm. (In the back of your mind like all airplane buyers, you've already got the silk scarf around your neck and pictures of your new "baby".) But the airplane is not a "baby", it's a piece of metal that is going to cost you many thousands of dollars in the future - so take your time and be willing to wait for the right one. It may be this one if the seller is willing and it may be the next one.
By the way, plane prices are a lot like used car prices. I want $5,000 for the car. I put it in the paper for $5599 or $5999. There's a chance that somebody out there will pay the higher asking price, but I can "settle" all the way down to $4999. Think about the AI an the "shimmy". You think the owner knew about these things. He already is thinking that he's got to fix them but it costs money. He can sell "as is" or fix and price.
This is not rocket science. But the more cold-blooded and casual you are about the deal, the better your pocketbook will look. Me, I hate Saturn dealerships with their non-negotiable car prices. Give me a good old fashioned car dealer and let the games begin. I give them that "I just love this car" junk and then when the money starts talking, I just walk away. They can't stand it.