Should we try to adopt wild kittens?

Question

Background

About 3-4 months ago, a wild cat gave birth to four kittens, likely somewhere near to our house. We first noticed them meowing and then managed to spy them playing in the overgrown bamboo behind our house, with the mother in close proximity (presumably keeping an eye on them?)

At first, any sort of movement, noise or eye contact would startle all of them and send them scattering, so we sought online advice for the best way to hopefully care for them. The general consensus seemed to be "place food out for them and gradually sit closer to it, paying no attention to them while they eat".

Over the last few months, we believe we have slowly begun to earn their trust. We initially had to put food out a decent way from our front door and have all the curtains shut (so they knew we weren't watching them) before they would eat the food. Fast-forward to the present day and all four kittens will now happily appear in the early to late evening for their daily feed.

By propping open the cat door (it was part of the house, we haven't owned any cats before), we have taught them to enter/exit through it and they will happily munch away on biscuits, wet food, treats, supermarket luncheon and tins of salmon (which they love). They haven't yet figured out how to use the cat door when it's closed (as in, they'd need to push against it to get through), even when tempted with treats from the other side. A few of them will allows us to pat them, but only if they're distracted by food, if we try to initiate without them being distracted, they all run away. They're also quite happy to be hand fed and sit/semi-sleep fairly close to us.

We made a little sheltered area outside for them, with a bed and protection from the rain so that they hopefully had somewhere to feel safe. They don't use it all the time, but we do occasionally catch them sleeping in the bed on our way to work in the morning

Both parents are still in the area, but much more wary of people than their kittens. We will occasionally spot them coming to eat the food, but any sort of movement, sound or eye contact will send them fleeing. We're happy to care for them as well, but they are probably too mature/wild to be domesticated. We'll hear the parents calling for the kittens from time-to-time, but we probably only notice it every 3-4 days at most

The current situation

My wife and I are in the process of buying our first house (we rent at present) and we are concerned about the welfare of the kittens. We would sorely love to adopt all four and bring them to our new house, but first and foremost, we want to what's best for them and both their parents.

I can't imagine it being too difficult to trap and cage the four of them, and we are keen to get them to a vet for a checkup, immunisation and appropriate desexing etc. (I'm not too familiar with the general procedure). We would then likely have to lock them in the bathroom with litter/food/water/toys etc. for a number of days, before letting them out into the house (as was the practice when my family had a cat in my (far) younger days), at least that's our plan so far

Our questions

1. Is it better to try and take the kittens with us so that they are fed and looked after? Should we leave them where they've grown up because they know the area and hope they can feed themselves (or someone else decides to feed them)? Or should we take them somewhere so they can be domesticated? (I'm imagining an SPCA-like environment for wild cats, but that may not exist, I haven't looked into that side yet)
2. If we do take them with us to our new home, what's the best strategy for ensuring they face as little stress as possible and have the best chance of accepting their new home?
3. If we capture and cage all four kittens, are the parents likely to freak out? Should we consider attempting to capture both of them as well? I don't know how protective mother/father cats are in the wild
4. Are there any general strategies for domesticating wild cats? We know about avoiding eye contact and trying to keep a low body profile around them so they don't feel threatened, but we aren't sure how to earn their trust further, or teach them how to use the cat door properly

tl;dr we want to adopt wild kittens and take them to our new house, how do we do that?

Answer 1

8-12 weeks is the critical age for cat socialization. You've already started the process and are doing fairly well, but I doubt you'll get much further with the kittens living outside and their parents still around. They really need to be trapped and the process finished before they get much older. The good news is this is (not coincidentally) roughly when they're weaned and their mom is going to ditch them soon anyway. All they need to learn is that humans (a) won't hurt/eat them and (b) will provide food, and we essentially replace mom on their minds. Four kittens will be a handful, but they are the perfect age for first-time cat owners.

The parents are well past socialization age, and based on their behavior, probably can't be tamed, at least without experienced help and a lot of time and effort. As first-time cat owners, please do not even attempt it.

The best bet is to find someone familiar with humanely trapping feral/stray cats. The adults, at a minimum, need to be neutered so they're not producing dozens of more helpless kittens over their lives, not to mention the various risks to their own health and safety. Check around for a TNR (Trap, Neuter, Return) or TNVR (Trap, Neuter, Vaccinate, Return) group in your area; they should be happy to help. Your local animal control authority, SPCA or vet may also help with trapping, especially if you're going to keep 4 of the 6 targets.