While working on my TE 510 I ended up pulling a little too hard on the spark plug cable and pulled it out of the cap & coil. Like in the picture below. I pushed the cable back in the coil and in the cap & the bike started and ran fine almost like it was designed to separate. My question is: Do I need to replace these parts, or is this designed to separate and be pushed back together?

Normally there is a screw-like terminal which threads into the cable. So you should twist the cable on until it is thumb tight. If you have spare length, sometimes it helps to cut 1/4" off the end so it is fresh.

You need to replace it you pulled the resister apart inside the cap.