Yes
Yes, small ones.
You can rent a tube with a bottom in it and tie it to your kayak. Its $5 to rent the tube and they have string to tie it to your kayak. This is what we do. If you get an open top kayak then you could fit maybe a 12 pack cooler on the back of it. If you get a closed kayak maybe a 6 pack size would fit in by your feet.
If you are talented enough to kayak with a cooler yes, if not I can suggest backpacks with bags of ice to keep things cold. Canoes and rafts fit the coolers well.
Yes. Encouraged actually. We pack 1 huge one and 2 smaller ones. Food and drinks and snacks for all day fun!
Yes you can. Just know that you run the risk of loosing it if you tip
Thanks! Your answer is awaiting moderation.