I recently started flying with our baby and I can only offer my experience.
Question 1: The plane is an A319 and the Main Cabin Extra seats are available for purchase. If I purchase those, will the middle seat also be blocked?
In our case, 8 of the 10 flights we've taken, AA proactively blocked the middle seat. As mentioned above, if flight is full or sold out, they will unblock and give it to a passenger. I have flights booked for next month and the middle seat was blocked off immediately.
Question 2: Do you recommend booking the Main Cabin Extra Bulkhead seats?
Didn't fly an A319, but on the 737-800 and A321s, we discovered that the bulkhead seats have airbags on the seat belts which prevented us from using the car seat we brought on board. We were able to switch to the MCE row behind us and use the car seat.
Question 3: Since I'm Gold and I'm traveliing with my Wife on the same ticket, we both get a free checked luggage but does the newborn also get a checked luggage?
Has already been answered.
Question 4: Am i allowed to bring another carry-on for the newborn? Or is the stroller considered a carry-on?
Has already been answered.
Question 5: What should I be asking? What I don't know that I should know or wish I knew?
All babies behave differently. We've been lucky that our baby has given us no issues while flying (crying during takeoff/landing, etc), at least so far. Still, we try and feed the baby during takeoff and landing to minimize their discomfort. Another thing to check is see which lavatories have changing tables, we discovered that not all aircraft lavatories have them.