As you already stated, your official payload is a little over 1500lbs. There are a lot of previous discussions on this forum which camper - if any - can be put on a 150/1500. The consensus seems to be: not a lot. A small, lightweight hardside camper or a popup will work.
I can not access the links you posted (probably because I am not in the US), but here is my comment based on what I can see:
1500-2000$ will not buy you much of a camper. Expect a lot of work and preexisting problems.
I seriously doubt any 12' camper can be put on a half ton crew cab, weight wise. Also you will need a long bed for a camper of this size.
Do not trust any stated weights unless you can verify them on a scale. Almost everything camping is heavier than you think.
You can travel overloaded to a degree. Just know what you are doing and you will be fine. That will not absolve you of (potential, remote) legal consequences, and you can not beat physical reality. Know your axle weights and tire loads, especially in the rear.
Your project sounds like a lot of work. Would you rather travel or build a camper, or do you have time for both?
Yes, many people do use the bathroom. But that question is probably as old as campers are. Some people will never use them, some only in an emergency, some can not imagine using a camper without. We are in the latter group, but there is no right or wrong here, just personal preference.
Best of luck, and safe travels!
Edit: removed Tundra half-ton claim. I was malinformed.
2014 Ford F350 XLT 6.2 SCLB + 2017 Northstar Arrow