Rehearsal

Not necessarily, but some drinks afterwards wouldn't hurt.

Nope! Rehearsal dinners are never necessary, but if you're rehearsing then it is typical to offer some sort of food.

A rehearsal dinner is only necessary if you have a rehearsal.

If you have a rehearsal, you need to provide some sort of food, even if it's just pizza or sandwiches. But you really don't need to have a rehearsal, especially with such a small wedding party. Just have your officiant tell them when to walk and where to stand, a few minutes before the ceremony.

There is no need if you have a small party and everyone knows what to do.

As long as you don’t do rehearsal you don’t need to do a dinner.

Our lineup + my dad and his mom. We had a rehearsal for 10 mins Andrew just talked through it with a floor diagram. We had a welcome lunch with 80% of our guests afterwards. It was vital to us to get people on a schedule (lunch was at noon, our wedding the day after was at 11:30am), and everyone got to meet and chat before so the entire wedding day was super laid back and everyone knew each other already. My husband's parents hosted.
It's definitely not critical and it's your wedding!

Usually after rehearsal you do one but I think with such a small party you could ideally skip it too. In fact it saves a lot of money skipping it when it's a lot of people but for yours it seems like it's nice to do also

It's really only necessary to have a RD If you have a rehearsal. As said above have a small set up like fruit and cheese trays or some finger foods and have a couple drinks. Wake up the next day ready to walk down that isle as you always dreamed you would. Good luck!

Nope!

You can do whatever you want though people will expect a rehearsal of some sort. I look at the rehearsal dinner as a thank you to the wedding party for taking time out of their schedules to do this for us. But you can easily replace the dinner with a small luncheon or provide some light snacks and refreshments.

Or you don't have to provide anything.

It's nice to, but not required in my opinion for such a small group. Could you go to a casual dinner after?