For water based paints, I spritz the roller with water, stuff it in a plastic grocery bag and store it in the refrigerator or freezer if I'm going to be needing to use it again in a few days. At the end of the job, I clean them. Take them outdoors and use a garden hose end sprayer (with the roller on an extension) and clean them. Aim the water to the outside of the roller; it should spin like crazy and spin the water & paint out. It will spin itself almost dry.

You'll have to live with a painted lawn until the next mowing...or wash the lawn down. I just let it go and clean up with the next mowing.

It's been eons since I rolled shellac; pretty sure that we tossed them when done.

Where do you dispose of the residue that comes from cleaning an oil based paint brush? I will be using oil based primer for some of my cabinets...

I throw away the rollers (usually use previously cleaned rollers) if I use anything oil based, and if a brush is needed, I keep cheap utility brushes for oil based and shellacs, and I throw them away too. For latex Paint rollers, I clean. Once the paint is all out of them, I also soak them in a dishpan with dawn dishwashing liquid and then rinse them well, and roll them in old towels until they are almost dry and then put them away. I also clean my good paint brushes well, and once they are totally clean, they get rewashed in dawn too, then rinsed well, and are hung up to dry. If I am finished painting for the day, or have to be gone part of a day and am not done painting, I leave both the roller and the paint brush in the roller pan, and I put the whole thing in a kitchen sized trash bag, and tie it shut, and then fold the tied part over and put it under the pan and leave it on the kitchen countertop, until I am back home and ready to finish painting.

Cabinets don’t get rolled. You’ll get stipple. They get sprayed.

I've known professional painters who store the rollers inside the same paint can they're using until the can is empty (then they throw away), note that since tinted paints are never the same tone (even if matched) the rollers might not be usable on a second can.

If you want to reuse water based paints you can clean them as ci_lantro suggested, but they will never be 100% completely clean.

I hate using cheap rollers, so I wash the expensive ones when using water-based finishes. For oil I'll store them wrapped tightly in plastic overnight during a job but then pitch them at the end. Brushes I leave immersed in thinner up to the ferrule until the end of the job when they are thoroughly cleaned and dried.

Paint thinner can be reused for a really long time by using the method described above where you let the solids settle out.