yes, you can use the old paint but, mix is good with a mixer attached to a drill (stick stirring will not work well).
Use a 5 gal. paint bucket and screen instead of a paint tray.
clean the roller until no paint comes out of the nap. If it's a cheap roller, just throw it away (not worth cleaning) the quality of the brush & rollers has bearing on the outcome.
yes, sand glossy surfaces prior to painting. You don't have to sand it down, just break the gloss and rough the surface for good adhesion. Wipe down the wall after sanding.
avoid peeling new paint by removing the tape before the paint dries too much or don't use tape at all and practice cutting in. You may need to change to a lower adhesion tape. use Blue Tape or frog tape not masking tape. Or let the paint dry completely and trim the paint line with a razor knife to separate the paint from the tape.