After I finish my match in a draft, is it okay to observe other matches?
It is perfectly acceptable to observe other matches.

If you are not currently playing, and you are not a judge, then you are a spectator by definition. There are a few rules governing spectators mentioned in the Tournament Rules.

Players may request (via a judge) that you not observe their matches. You may not make notes while drafting. You may not place bets on any portion of the game. You may not provide assistance to players in a match.

You are allowed to collect and share information in order to gain an advantage. This is called scouting. Some people dislike this behavior, but it is legal nonetheless.

Finally, I want to note that at Regular REL (which includes Friday Night Magic) the "continuous construction" option is allowed unless the tournament organizer explicitly says otherwise. This means that you can sideboard between matches. This rewards scouting. However, it also makes the game more fun for newbies who may want to improve their deck as the evening goes on. Talk to your tournament organizer and explain the upsides and downsides. Help them make an informed decision.