On part 1 of your question it really depends on the foul and when it occurs, but typically you would be referring to a personal foul or an unsportsmanlike conduct. Those can be assessed on either the try or the ensuing kick off at the option of the scoring team.
However, say there was a foul by the nonscoring team that was called, unless the act warranted a personal foul, that penalty would be declined by rule.
