@Gloria Rostron I don't want this to come across as patronising, but I think you'd be better served spending your time doing a lot of research into the house buying process (both the legal and financial side of things) and also getting your ducks in a row in the property you are currently living in. MoneySavingExpert and the forums there are packed with info that you'll find useful.
House buying is a bit of a mysterious process, especially to a first time buyer. But after having read this thread, I am a bit concerned that you could be taken for a ride here. Few bits of advice/things to think about:
1) Do you have the £60k (I think it was) deposit money sitting in your bank account right now? Or is this the amount you're expecting to get from selling the house you're currently living in? If this money is coming from the sale of the house you're currently living in, there is no point continuing to look on Rightmove/Zoopla or emailing agents with offers because you aren't in a proceedable position (meaning you're not financially ready to purchase a new property). Vendors and agents won't entertain you until you are in a proceedable position, even if you are offering over asking price.
2) Probate is only something that needs to be worried about if the owner of the property you are buying has died and the property is being sold by their relatives. If you bring up probate to a conveyancer when you're actually purchasing from vendors that are alive and kicking, they might ask for paperwork that doesn't exist/start making irrelevant enquiries. It will confuse things. Probate only needs to be mentioned if the property owner has died.
3) I would expect your conveyancing fees to be a couple of thousand pounds (excluding any stamp duty payable). Anything substantially more than this is expensive. Please don't get ripped off! As you're a FTB and unfamiliar with the process, you'd also benefit from using a conveyancer that doesn't charge for every letter/email/phone call.
4) The situation with your current property sounds v. complicated, and I'm sorry it's come about as a result of sad circumstances. It also doesn't really sound like you have anyone to turn to in your "real life" for advice on handling it, so I think you need to get some solid advice from professionals. My two take aways from what you've said about this are: 1. Make sure you get your property valued by an independent RICS accredited valuer (not an estate agent) to get a true idea of what it's worth. I really hope it's not the case, but I would hate for your uncle to be convincing you that it's worth less than it is so he can make more money out of it. 2. You mentioned something about your uncle paying off the mortgage on the understanding that he would then buy the property. I can't comment too much on this because I don't know the ins and outs of it, but, again, I would hate for your uncle to have "helped out" by paying the mortgage only to use it as leverage to his own advantage later on. MSE forums are packed with stories of families/spouses/friends shafting each other, so I'm not trying to bash your uncle, but these things do happen.
Hope some of this might be helpful.