Questions on flying with infant

FTM here and first time flying with my 10 month old. I have some questions if anyone could please answer that would be great!

We are flying Spirit Airlines, we have the big front seats there and back, only about a 2 hour flight.

1. She will be “lap child” however we plan to bring her car seat plus her stroller for the rental car at our destination. Are we allowed to “check” both/ bring both along? Will they make a big deal that she’s not riding in the car seat? Does it cost extra money to check these items?

2. We normally have bottles with water, and then bottles with just the powdered formula in her diaper bag so it’s not premixed. What would be easier through TSA?

3. Will they allow small toys to occupy her on the plan?

4. Will they allow Lysol wipes? Or santizing spray? Does it have to be a certain size?

ANY OTHER TIPS APPRECIATED