Measure 24 links of the chain under tension; if it's much over 12&1/16", you need a new one. The new chain may skip over your freewheel if you don't replace that too, or at least wear out too quick.

Pff to replacing the tyre, just cause the tan rubber's perished... it does nothing but protect the side of the casing from abrasion; Conti GPs have virtually no rubber there... I lost more than one with plenty of life left thanks to sidewall damage. Replace it only if it has any bulges or expands alarmingly as you approach 100psi. My Conti Supersports are so old and perished I was able to scratch off all the moulded-in writing off the sidewalls, but the casing and tread are just fine.

As for getting the cable out of the lever, hit it with WD40 and grab the cable just where it comes out with vice grips and twist in the direction the strands go. If that doesn't work, the cable may break off where it meets the end; then you should be able to punch the end out. Trying to drill it out from the other side would prolly be a bastard.