being used by police officers when apprehending criminals, "you're nicked".

I heard over the weekend that the term "nick" for prison (and presumably thence to "nick"= "arrest") is derived from St. Nicholas being the patron saint of prisons. Not sure I believe it yet.

With multiple meanings for nick/knick you could get: "Nick (of the NY Knicks) was nicked for nicking knickers worth half a knicker and ended up in nick". Stretching the elastic a little further, the knickers might have been damaged by a knife and hence been "nicked" in another sense.

"buy it or nick it from Woolworths"
always sung that as "Woolies". No one in UK calls it "Woolworths".

Rod