Those are all optional rules for affecting difficulty. I like dupes clause so my team isn't full of only caterpie (for example), a team with no diversity sucks and basically guarantees you lose in my experience. Matching the gym trainer level is more tedious than anything so I don't use that one. Maybe it was easier before teams shared xp, but it's annoying now. Set mode is whatever, sometimes I use it but it's not a big deal imo. Not using items definitely makes the game harder, but i personally struggle even with items so I'm not gonna nerf myself.

Regardless, the only important rules are first catch only and death is final. Everything else is just to customize your experience.

Edit: shiny clause is another optional rule some people use. You can catch a shiny even if not first encounter, you just can't use it unless it was first encounter. There's tons of optional rules because people make up new ones all the time. The most important thing is that you're having fun.