Flying with baby!! Questions!

MaKayla • First time momma to a handsome preemie baby boy ❤️😊
So on November 11th, our family has decided we're going to Florida to visit family. I've never flown with a child being as this is my first baby, and I've also only flown once before this. I have a ton of questions!!
How do you gate check a car seat?
Do they allow the base to the car seat to be checked as well?
What about baby bottles, can I have the 6 oz of water in his bottle?
I plan on him going as a lap baby, has anyone else done this? 
Best way to help baby's ears? Bottle or binkie?
We are planning on flying with Allegiant air, I've never flown with them, only Southwest. 
Anyone have rates on them?
How bad is airport security with a baby?
They say no baby carriers allowed. So how would I get to take my shoes off and carry him, a car seat and diaper bag? 
Soooo many questions unanswered on their page!! If anyone can help with any answers I'd appreciate it!!