Yes, Eurail will be valid here. And good value because the children’s passes are free. 

It will be the same trains you take whether you buy tickets or use a pass. So any difference in itinerary you see now is down to the journey planner not finding all the trains. 

You’ll need to budget for reservation fees (including for children) on the three journeys that are in France.

See here for costs https://www.seat61.com/interrail-and-eurail-reservations.htm

Don't know why you are comparing 4 single journeys to a 10 day pass?

If these are your only journeys, a 4 days in a month railpass for 866 $ and a single ticket Strasbourg to München would be cheaper (if you are really staying in Strasbourg for a month).

Be aware that you need to buy mandatory reservations when holding a railpass (not in Switzerland). E.g. 10 € per person for Paris to Strasbourg.

Interlaken to Paris with only one change is also possible with a railpass, but the reservation fee for the direct train from Switzerland is very expensive (39 € per person). It would be much cheaper to do the border crossing by regional train. But it's possible to go by direct train (with one change from Interlaken) with a global pass, too.

Thanks for the replies @ralderton and @Hektor they are very helpful!

I'd definitely get a pass. You'll move around Interlaken and Switzerland for sure : as tickets are expensive using a pass day is good value.

You get 25-50% discount on mountain railways and boats on Lake Thun and Brienz are fully included (although they don't run often in autumn/winter).

What are you planning to do around Strasbourg ? It's a beautiful city but 1-2 days is more than enough.

Thanks for the reply @thibcabe