Read these articles if you haven't already:
For example, the following CANNOT happen.

It's because B happens before D and D is included in the snapshot. After P1 takes snapshot, it has to send its marker message to P2 before doing anything else. Given that condition, D cannot be included. If it is, it's the violation of FIFO.

A cut is a "time frontier" going across a Lamport diagram, dividing it into "past" and "future"

An event is "in the cut" if it is on the "past" side of cut.
A cut is consistent when, for all events F,E that are in the cut, if F->E then F is also in the cut.
So the inconsistent cut would look like:

And then consistent cut would be:

If you take the set of events in Chandy-Lamport snapshot, and you make a cut, it's going to be consistent.