Honestly, some of this will be postnatal hormones where your safety drive for the baby is in absolute overdrive.
I also had arguments like this about things like formula preparation. Stuff like whether DH had touched his jeans halfway through making it and hadn't washed his hands again. Even though this is literally the recommendation, it's total overkill because it doesn't need to be THAT sterile when you're feeding pretty much straight away, but it felt like a life or death critical issue to me at the time.
See if DH can give you a bit of leeway to just be OTT for a bit, in the knowledge you will probably relax about things soon. Get him to talk to any friends he has who are involved, kind dads who have probably experienced this stage before. At the same time, try to give him space to make mistakes. You will both make mistakes, it's part of parenting and it's very helpful if you don't jump on him the moment he does, because culturally, there is already so much bias in the direction of mums being the "default parent", and long term you don't want this, even if your brain is currently insisting that you need to have total control because he gets things wrong.
WRT the car seat, don't stress about this now. First of all 15 months is a long way away and babies' growth often slows down.
Secondly, he's bound to want a whizzy spinny one, because a lot of men love a gadget, and they ALL rear face up to 105cm which is about age 4. The seats from 9 months which are only forward facing just aren't really sold any more. He's out of date in assuming this is the next type of seat to get, but when you get there he will find out what's currently available and you'll make a decision together. Don't worry 
If the obsessive thoughts about miniscule details and compulsive need to correct things continue past about 6-8 weeks postpartum, or they are taking over your life to the point you can't sleep or can't let DH do his thing, talk to your midwife/HV/GP as it might be postnatal anxiety.