Obviously without driving yours nobody else could say that's OK or not OK. I've got a 2018 1.3S, the gear change isn't as quick, smooth or sporty as the 2003 1.4SE I used to own, however I wouldn't describe it as notchy, I haven't had any specific issues with it, just noticed it's not as effortless as the old one, it is perfectly acceptable, just not great like the mk1 Jazz, I've driven much worse brand new cars (and better).
The door issue sounds like the striker plate on the door frame needs slight adjustment and possibly the hinges and/or the door catch as well, this is a simple 5 or 10 minute job.
I'd get the dealer to adjust the door and at the very least give you an opinion on the gerachange, there may be some adjustment they can do there as well to improve it.
All the best