Usually recommend Evian or low sodium content mineral water but you can boil the local for cooking.
Don't think they'd insist upon a car seat but I expect you'd feel happier with one - can you prebook a taxi with one from the airport ? (We did in Majorca last year )
Large pushchairs (ie. not umbrella or flat fold) usually go in the hold and are checked in but unlikely to be charged as excess, but may vary by airline. If you are really lucky you may get to take it to boarding gate. However unless you arrange as you have it tagged to collect from aircraft it may not be available until the baggage hall the other end.
Most brands are stocked in Europe albeit sometimes under a different name, but take some to cover the first few days. tbh changing brand for a short while probably won't hurt and you could keep him in Swimmers (either disposable or reusables) for much of the day anyway.
I used their drinking water for bottles and cooking, once it has been boiled it has killed off any bacteria Some mineral water has too high mineral/salt contents btw.
Taxis won't be adamant about you having a car seat it is just whether you wnat to take the risk. I take my car seats and my pushchair with me and have never been aked to pay for the extra. One time I went with 3 suitcases, buggy, back pack and car seat and no one batted an eyelif.
Never paid extra for a buggy. I have always had to leave mine at the bottom of the steps to the plane and collected it at the carousel.