I just installed an led dimmer. It didn't have pigtails like the ones you have, so hopefully you won't need the wire nuts and can save some space. Check the instructions for your dimmer. On mine the polarity didn't matter.

Correct. Some dimmers have pigtails like your old dimmers and some have screws. Just wire the new dimmers like the old ones. You must buy dimmers that do NOT require a neutral wire. The Lutron DVCL-153PR-WH is a very good dimmer. If you use that dimmer, be sure to break off the side tabs before installing them as described in the instructions.

Have you checked to see if that installation complies with electrical code box-fill limitations? It's hard for me to count but there seem to be quite a few wires in that box.

The person who installed this switch:

doesn't know what they are doing.

There is too much of the insulation stripped off the wire and the red wire is wrapped the wrong way around the screw. It should be clockwise so that as the screw is tightened, the wire gets pulled into the screw instead of pushed out.