Those of you that have flown with an infant

Anyway, I have just a few questions.

1) For our personal & carry on, is a diaper bag considered our carry on or is that something that we can have on top of our 2 items?

2) What are some things you wish you brought but didn't or didn't see on the lists online?

3) what made your life so much easier? (I do plan on baby wearing because I know that's a plus) and I will try to request baby crib/cot on plane for my regular flight if available 

4) I believe for space A baby is required to be in car seat (we don't have a choice between lap or extra seat.. I think. I'm going off what I've heard, still need to go to the terminal to ask all my questions) but for those of you who "lapped" do you regret it or was baby wearing okay? (There will be both me and my spouse) I know traveling with the extra seat is the safest but none of my family has done that, and we may, but we are keeping our thoughts open.

5) What did you gate check, check, and Carry on? Depending what regular flight I choose sometimes we can free bags with leisure travel so bringing many things isn't really much a hassle cost wise.

6) any other tips are welcome, I'm just starting all my research and brain storming. 

Thanks!