1. You need a thin cone spanner and an adjustable spanner (a box spanner is better than the latter if you have it - one of those dumbbell spanners is good). Loosen the lucknut while holding the cone. Now screw in the cone to eliminate play but still allow the axle to turn freely. Hold the cone steady and tighten the locknut hard against it. This will take a few attempts to get just right, and you may need to hold the locknut on the opposite side with a third spanner (and your knees) to stop the axle turning, or pop it in a vice.
I'm assuming you have nutted axles; with quick release hubs there should be slight play left, reducing no zero play when the wheel is installed in the frame - the QR compresses the axle and rtakes up the clearance.
2. Assuming it's a quill stem, which will have giant headset nuts below it: loosen the central bolt by a turn or two and then hit it hard with a mallet. The stem should come loose and you can adjust the height. Make sure to get it central and not to go above the "MAX" line. Then tighten the bolt hard to keep it there. Typically you will find that the stem has seized if it isn't taken out and regreased annually. Do not touch the giant nuts!
