All are ok and natural? Or how would you say?
We should always bear this in mind.
We sxpect everyone to fulfill their responsibility.
We call for everyone to be common-sensical. or We call for everyone to be prudent.

Question

All are ok and natural? Or how would you say?
We should always bear this in mind.
We sxpect everyone to fulfill their responsibility.
We call for everyone to be common-sensical.  or  We call for everyone to be prudent.

Answer

The first two are correct.
 
For the last two you should use "ask " instead of "call"

Common-sensical is correct, but in this case it would be more natural to say  something like " We ask for everyone to use their common sense"

Common-sensical isn't a word we use much in english