Hi Jonny welcome to BW
It sounds to me like you and your wife have started out great
Yes your baby is young and does want and need to be close to you, totally normal and the time you spend with him will build a fantastic bond so I wouldn't worry about that at all. For babies to learn to sleep independently they must first learn they can totally trust in their parents to respond to their needs, responding to your baby's needs actually makes them less needy, rather than more. Yes it's true that you will want baby to sleep independently and it is a joy to see them go to sleep with a smile, happy and confident, knowing that you are not abandoning them but rather giving them space to sleep and rest, however at 8 weeks it is still early days. Very many parents choose not to sleep train until later. I started quite early with my LO and he slept independently by 8 weeks but it's important to note that I have still been needed very many times over the last 2.5 years.
Baby groups often clash with baby's routine, it's just one of those things. I agree it is important for your wife to get out and about if this helps her to feel more sane, a happy mummy is far more important than sleeping in a cot at home
In time baby's routine will alter, making the groups more easy to fit into the routine, and then alter again making it tricky and so on. You can decide together which groups and times you feel are needed to get the right balance for your family, weighing up sleep needs with social needs etc. In my son's first year I kept him home mornings to retain a good morning nap in his cot and went to groups or shopping etc in the afternoon (leaving the house in time for one nap in the car on the way there and laving the place to time CN on the way home), in his second year I switched to morning groups as these fitted around his one nap more suitably.
I would say if you want to establish a 'better' routine for day sleep you should try to keep each day very similar. Many people choose one nap to take at home in baby's cot to ensure baby can sleep independently at this time and get a good long restorative nap, when baby is older and some of the naps are dropped this one at home in the cot can be the one that it retained to keep LO well rested (this is what I did). If all naps are going to be out and about then really you need to expect LO to find it tricky to nap at home. There is nothing actually 'wrong' with this, but know it is likely to happen, you set the habits and LO follows them. So if almost all naps are in the sling, car, stroller then that's what baby will expect. You could for instance nap him in the pram at home on days that they don't go out if you find this acceptable.
Mine never had the habit of sleeping in a pram, only in his cot for morning nap and the car for afternoon nap, so it was almost impossible to take him out in the pram and expect him to nap - he just cried because it was not what he expected.
Your questions
1. The crib in your room sounds ideal. He will not get confused at all if you put him down for naps there - in fact I used to put mine down in a travel cot in the living room until he suddenly refused, all sorts of crying, then I realised he wanted his proper cot where he slept at night, so he napped there from 10 weeks (it may be a similar case with your LO that he wants his night bed). The SIDs guidance suggests baby should be in the same room as you (for naps and nights) until 6 months, you need to be comfortable with your choices. I was on edge the first few naps then relaxed and trusted the monitor, I could hear him breathing over it.
2. Babies really do need their sleep. But mummy needs to be healthy and not feel totally trapped at home. So like I said before a balance is needed to attend to everyone’s needs as much as possible with a little compromise on all parts. As a thought, your wife may choose to attend baby groups and do chores out and about in the mornings but be happy to stay home in the afternoon (maybe nap herself if needed) to create napping habits at home too. A 45 min sleep is not restorative and is by no means equal to a good long 1.5 - 2hr nap, it can indicate inability to transition from one sleep cycle to the next (ie not yet learned to to this) or can indicate UT (under tired) for that nap. Short naps (even if caused by UT) during the day can lead to OT (over tired) by night time which can disrupt night sleep.
3. It's not really about if sleeping in a sling is 'bad' (although some slings are not so good for baby's back and development, ditto car seats, swings and other place LOs like to sleep that are not their cot or a lie-flat stroller) it's more about if you and your wife are happy and able to keep this up. When you get to the point of it not begin ok with you, that's the time to begin sleep training and break this habit. Remember that babies start to get heavy even in a nicely fitting sling it can start to take an effect on your own posture and back ache sets in. I'd suggest sleep training before this is the case, starting at a time when you feel you have patience and energy levels needed to put the time in, rather than waiting until you feel 'desperate' and crippled with back ache because through sleep training you will still need to lift and hold your baby, bend over the cot etc so I wouldn't suggest waiting until you are at the end of your tether, you know? Everything can be changed later, there isn't a deadline, there will always be support on the boards whether you sleep train now or in 3 months, 12 months whenever, so really it is your choice.
I hope this helps with your questions. Do feel welcome to ask more.