Congrats for your baby. I read your question regarding water & gas problem for newly born baby. My baby is masha Allah 2 months old now & we also suffered the similar problem. I'll give you my first hand experience insha Allah that will help you.

1. For Gas problem:

If your wife feeds him naturally then wait for 30 seconds after feeding & put him/her on shoulder to make the baby burp. You have to pat the back of your baby slowly which will help in releasing the gas out.

If you are using powder milk also alongwith that then I suggest Similac (which I am also using). Keep some mineral water bottles in home handy & 1 flask which can keep the water hot for long time. Now boil the mineral water very well & keep it very hot in the flask. You have to feed your baby after every 2 hours during first trimester which you should always remember otherwise he/she will have renal failure. Secondly, the proper way to make powder milk for baby is to put 1 scoop of powder to 60 ml of water or 2 scoops to 120 ml of water. Put this in bottle & shake very well in the sink as it starts coming out of bottle. Now pour this milk in a wide glass mug to make it cool or just luke warm for baby to drink easily. After every feed, I immediately make another bottle for my baby & when he is about to wake up I pour a little boiled mineral water to make it luke warm for him, in this way he doesnt cough.

2. Water:-

My baby was getting constipated & was having difficulty in passing the stool. So, I give him just 2 teaspoons or 4 teaspoons of water once in a day everyday. This makes him use his excretory system easily & he doesnt put that much of force too. Also keep Johnson's Petroleum Jelly with you all the time & whenever you change diaper put that jelly a bit outside his pvt part to keep the area soft.

Note: I have given you remedies which I using on my baby & I am quite at peace with this.