I’ll try to answer as best as I can, though I’m not a very experienced rabbit owner. Hopefully others will have suggestions too.
1 As far as I know wheezing is not normal for rabbits. Try to find a specialised rabbit-savvy vet and get a second opinion. Rabbits count as an exotic species, and the vet will need to specialise themselves in exotic species to treat them properly. This can make it difficult to find an experienced vet, but it’s vital for your rabbit’s health.
2 Every rabbit is different, but generally rabbits calm down as they age and after spay/neuter. Most rabbits like to be petted (at their own time & conditions), and some will like laying next to you. It’s very rare that a rabbit wants to sit on your lap or on top of you. Most prefer their freedom and hate to be held. They can also have their own daily schedule, and may not be ready for cuddles when you’d like it. My rabbit is only cuddly from 10 in the evening. The rest of the day he likes to do his own things, and he prefers to be left alone then. It also took him a while to warm up to me, after a year he became more cuddly and now he’ll lay next to me on the couch for hours.
This is a website with good tips to improve your bond: http://rabbit.org/bonding-with-your-rabbit/
3 Most rabbits do better with a bonded rabbit, but there are always exceptions. If you’re away from home a lot (work/school etc), it’s advisable to get a companion for your rabbit. It’s a decision which you’ll have to prepare for: getting another rabbit will take more time and it will be a greater financial burden. It can be tough to find the right rabbit, and bonding can take months. I think it would be best to adopt an adult rabbit from the shelter, because their personalities have already fully developed. It’s always a surprise with a baby, and if their personalities don’t match you’ll have a problem. Most shelters have “speed dating” sessions when adopting a rabbit for bonding, your rabbit can decide whom she likes during these dates. You’ll have to wait until her hormones are out of her system (at least 6 weeks after spay). Rabbits pair best with a spayed/neutered rabbit of the other sex, size or breed isn’t too important for them.