For the life of your chems, well, film developer should be used one-shot. Paper developer you can tell when it's bad by any of the following:

-it visibly darkens. If your developer looks more like motor oil then it's probably bad. There are exceptions (Ansco 130 comes to mind).
-your prints take more than 50% of your total developing time to begin image formation
-you have to increase your contrast filtration and/or increase exposure time to maintain good blacks in your prints from the same negative

For fixer, there are formulas out there from manufacturers on how many square inches of film/paper per liter of working solution. A bit of google searching should turn up results.

I would assume that the distilled water wash is being used for roll film, not for paper. That gets pretty impractical pretty quickly, especially if you're printing bigger than say 5x7.

Diluting developer does several things. It extends development time (which in your case, given how hot your water is, would be a good thing). It also serves to reduce the activity of the developer, which helps to control contrast (especially with the highlights, which develop first and keep developing throughout the process because there is the most activated silver in the highlights). If you have a very potent, active developer like D-76, it is very easy to get blown-out highlights when using it straight or even 1:1 because the developer is very strong. Other people here may offer you better advice on what dilutions of D-76 to use - I don't like it and don't use it myself so I can't comment beyond the basics.