Hi!
Welcome to the forum and congrats on your new arrivals!
Firstly, young bunnies should be separated, as while all baby bunnies get along happily, at around the age that hormones kick in (which can be anywhere from 8 weeks to 6 months), they are very likely to start fighting. This is doubly important for male/female pairs, as they can start breeding from 12 weeks. You need to separate them until they’re both old enough to be spayed and neutered.
Most vets will neuter bunnies from around 4 months, depending on their size, weight, and whether the testicles have dropped. Generally, if a bunny is over one kilo, most vets will feel comfortable neutering.
Make sure that your vet is rabbit savvy – if they tell you to fast the rabbit before the op, that’s a big sign that they don’t know bunnies, as bunnies should never be fasted before ops.
A female can normally be spayed around 5-6 months. It’s really important to spay the female as well, as rabbits have very high rates of uterine cancer in unspayed females.
Second questions – Most rabbits hate being picked up. If they don’t like it, insisting on carrying on is only going to make them not trust you. It is important that you’re able to pick them up in emergencies, and it sounds like you’re able to do that, so I would leave it there, and from now on only pick them up when you really have to (a nail trim, to get them out of danger quickly, etc). Most rabbits prefer to socialise with you if you sit on the floor with them, then they’ll come over for pets and attention.