Cleanng a brush used for water-based paint, with soap or not?
I get observably better result with dish detergent - less partially dried paint bits left stuck in the brush.

Detriment, if any, of very hot water might depend on brush construction. I doubt it would "dissolve the hairs" but it might damage some of the plastic bristles typically used for latex paint brushes. I prefer lots of water to particularly hot. I start rinsing cold (usually at the outside tap) and move to warm water and soap inside after getting the bulk off outside.

Extremely thorough rinsing is required whether or not you use soap. I normally do a crude rinse, work some soap into the bristles (with dilute paint still in the brush), and then proceed to the serious rinsing. If any color comes out of the brush, it needs more rinsing. If your rinse procedure is thorough enough to get all the paint out, it will get all the soap out. If it's not, you might as well use disposable brushes and not bother washing them at all.