I have two questions concerning the LFPF (for etale cohomology).

Is there an easy 'explanation' of this statements (that could be understood by students)? In particular, I would like to get away with a short and 'simple' list of properties of the cycle class map, and I want to make the linear algebra part of the proof as 'conceptual' as possible.

Is there an 'easy' proof of the non-proper version of the formula (that involves cohomology with compact support)?

I do not plan to give a complete proof; I would rather like to tell how to deduce the statement from certain 'basic' (and 'motivic') properties of etale cohomology (possibly, omitting some details).