Rear wheel sideways "play"

wrong. as for bearings, tight it has to be. in case of cup and cone, where you set the tension, it has to be tight but not so much as in 'it makes you feel the balls through the axle' kind of thing. you'll notice once you try, but no play. once you got past that point, give it a tad more and try spinning the axle.

a bit loose is loose and will be much worse under load. a bearing with play rattles itself to death in no time.

im talking about .1-.2 mm here,
with plenty of services (wipe, degrease and re-lubricate with finishline teflon bearing grease) ive had no problems, hubs on about 4000 miles,cup and cones are still ok and bearing are just starting to dull down a bit
will replace cup,cone and bearings soon though