Hello, and welcome to paw talk!
First of all, that's awesome that you are doing your research before hand!
To answer your questions...
1. Bunnies I think can be more expensive than people expect them to be, but in my experence it's a managable amount unless there's an emergency. Yes exotic vets do often charge more than normal vets. As an example, I pay $50 for a general check up for my dog, and $80 for a rabbit because they need to see an exotics vet that has experience with rabbits. Spaying or neutering can be up to a couple hundred, but if you adopt it should already be fixed. Rabbits in the US don't need shots like dogs and cats do, so you don't have to pay for that. So on average, I pay $80 for each of my rabbits to get a yearly check up. Sometimes things come up like they get sick or hurt and that can get expensive, so I'd suggest saving up some money in an emergency fund just in case you ever need it. How much you pay will really depend on the vet you go to and the area you live in as well. I've seen a pretty wide range of prices between diffrent vets. Usually vets in the city are more expensive than in other places because they have to pay higher rent.
For food, I spend about $50 on hay once every two months or so. I buy hay in bulk online, so that price includes shipping. Depending on where you live, you may be able to find a farm that sells hay very cheap. Unfortuantly I live in the city so that wasn't an option for me. But keep in mind that I also have 3 rabbits, so what lasts me two months might last you three times as long. Pellets I don't remember the exact cost, but I wouldn't say more than $15 for a 10 lb bag. I only feed my rabbits a very small amount of pellets so a bag lasts me a long time. I also spend a little bit each week on them getting them fresh greens at the grocery store, maybe $10 a week, or less? Some of the greens I get them are pretty cheap, around $1 for a lb or even less sometimes. I guess those prices would also depend on your local store.
Other than that, I spend money on them getting them toys and you will need to get supplies like a litter box, water bottle or bowl, food bowls. Depending on what type of litter you want to use in the litter box you may need to buy that. I use Yesterday's News litter, but will sometimes just use left over paper or grocery bags if I run out of litter.
2. Yes you can use fleece for rabbits. I use it for mine, just not in their litter box. My rabbits are all litter box trained so the fleece is more to make them more comfortable, but it's nice because it's easy to clean and reuse if they have any accidents outside their litterbox.
3. I use to have a 2 lb netherlands dwarf bunny, and still do have a 2.5 lb lionhead. Neither of them were ever able to escape from NIC cages, even when they where young. The only thing I would be careful about is that I've heard that they changed the sizes of some of the cubes, and made the spacing between the bars bigger. I have a huge stock pile of older cubes so I didn't really look into this much, but I guess it was a problem for some people who where using them for guinea pig cages. I had a link about it but I can't seem to find it now. I'll post again if I do or maybe someone else will know more about it.
I think I answered everything. If I missed something or you have any more questions please feel free to ask!
And if you haven't come across this site already, it's great for learning about keeping house rabbits.