do you need reservations for Institut du Monde Arabe

During the week, probably not (but recommended). On Friday and Saturday, they would be essential, because not all of the tables are along the side with the view...

I'm not sure this plan is doable at all.

Have you checked the times of the boat rides? I looked at several of the major companies and in off season the latest boat is at 10pm - in some cases 9pm.

There's no way you could have dinner at Tour D'Argent and get there in time for a 10pm boat. In fact, I would assume you would still be finishing dinner at 10pm.

Now - I didn;t check every boat - and thre may be one later - but I can;t imagine rushing to get one that late at night would be an enjoyable end to the evening.

Agree with the idea to do the boat ride first, then have time for a relaxing dinner.

This web site has a menu listed: www.bestrestaurantsparis.com/restaurant-
paris/detail/la-tour-dargent.html