A few thoughts for you. I'm sure others will have different comments because some of your questions will have different answers based on time of year you are thinking about going, what you are camping in, what type of loop (preferred, non preferred) you are in and how comfortable you are with camping. To that end, here are my OPINIONS and experiences.
I have never seen an alligator in FW. I have stayed there many times over many years. My parents go for a month every winter and they have never seen an alligator. And they have been going for a number of years as well.
You can't swim in the lake, but there are 2 pools. Not as fancy as the hotels, but it is still nice. I have heard many comments about why you can't swim in the lake. No lifeguards, too many boats, etc. I'd rather swim in a pool anyway.
We have stayed in loop 1400, which is a preferred loop (I think) and I never have had to wait for too long for a shower. I mean, maybe for a few minutes, but I guess it depends on the time of year.
We also really haven't had too much trouble with other campers. For the most part, people who camp respect those around them. And besides, at the end of a Disney day, I'm really tired. I can sleep through just about anything!
In the end, I would say that FW is a great way to be at Disney. I've stayed in the YC, BC and GF and had noisy neighbors, been woken up by people in the hallway or pool. I love FW because it is great to be outside and not limited to a room and balcony. Good luck with your decision.