Swiss rail pass

a) Swiss Travel Pass prices are per adult, with no discount for traveling together.

b) Yes, that's certainly allowed and not unusual. We often recommend catching the French TGV train from Basel for a slightly faster travel time. But for your plan, catching that train at Zurich and buying the advance-discount ticket from that point might come out cheaper. Check prices for the whole route at www.sbb.ch.

c) Yes, those trains are covered but none of them are in your route plan. Seat reservations cost extra and are either required or recommended for the panorama cars. On the Golden Pass line, it's the Zweisimmen-Montreux section that recommends a reservation.

Why stop in Interlaken? You are going there to see the magnificent scenery of the alps so why stop in Interlaken (which is not in the alps). Continue that day onto at least Lauterbrunnen (20 minutes additional) and either spend your night there or better yet just keep on to Wengen and spend 2 nights there.

Agree 100% with Tim. Go from Zurich to the Lauterbrunnen Valley, stay in Wengen, Lauterbrunnen or Murren. Bear in mind that Jungfrau can be clouded in. Sometimes when that is the case, it can be clear at Schilthorn. Schilthorn is included in the Swiss travel pass, I believe, Jungfrau is half price. Also, I spent three days in Luzern. Love it, love it, love it. I'm not sure about the swiss pass with Mt. Titlis, but Mt. Rigi is included in the Swiss Travel Pass.

The Swiss Travel Pass gives a 25% discount on the Jungfraujoch, a 50% discount on Mt. Titlis, and covers 100% on Mt. Rigi.

Here's the transportation map:
(Dotted lines mean 50% discount. A "1" in a circle next to the dotted line means a 25% discount. Solid lines mean 100% covered.)
https://www.sbb.ch/content/dam/sbb/de/infotexte/uebersichtskarte-sts.pdf

Day 2 and day 3 stop in Wengen, better than Interlaken.
Day 6, If you are going from Luzern to Paris, via Zürich is not the quickest route. It is about 1 hour quicker to go Luzern - Basel - Paris, the train from Zürich stops at Basel, and Luzern to Basel is the same as Luzern - Zürich.

Be flexible on the days for your mountain trips (Titlis and Jungfrau), depending on the weather, pick the best day to go up.

c) Interlaken to Luzern is one half of the Golden Pass route, you are doing this on day 3. The other routes too far from where you are staying and not convenient for this trip.

I assume you are flying into Zürich, and Day 1 is actually Zürich airport to Interlaken? If not, and you are arriving by train or road, via Zürich may not be the best way.