I've a question on Chum.

The one subroutine on chum says: "The next piece of ice the Runner encounters during this run has +2 strength. Do 3 net damage unless the Runner breaks all subroutines on that piece of ice."

To get this right, does that mean, if the Runner breaks this one subroutin on Chum, there are no 3 net damage dealt from the next encountered ice, even if he does NOT break all of the subroutines on this one?

And on the other hand, if he does not break the subroutine on Chum, the 3 net damage are not dealt until he has finished the NEXT encountered ice?

You are correct.

A similar question: if you encounter Chum, choose not to break it, and then jack out does the 3 net damage take affect? Of does that only happen if you choose to encounter the ICE and then cannot break it?

papy72 said:

This is answered in the FAQ:

Does the Runner take damage if he jacks out after
encountering a Chum and not breaking its subroutine?
No. The Runner has not encountered another piece of ice, and
so the subroutine on Chum has no effect.