Planning one day in Montreux - Itinerary help

Hello,
I will be arriving in Montreux from Zermatt by train in the morning and will be staying that night in Montreux.

Planning to do the following in one day:
- Chillon castle (One way by boat and another walk by walk)
- Rochers de Naye
- Notre Dame cathedral in Laussane
- Vevey – Chardonne – Mt-Pèlerin
(or)
Territet – Glion
(or)
(Montreux–) Les Avants – Sonloup

Questions:
1. Is this too much for a day?

2. When is the good time in a day to go to Chillon castle and Rochers de Naye?

3. Among Vevey – Chardonne – Mt-Pèlerin, Territet – Glion, and (Montreux–) Les Avants – Sonloup, which one should I choose?
I'm looking for best view and nature to see?

4. We'll be travelling to Paris from Montreux the following day and planning to go to Notre Dame church there.
Given that, should I go to Notre Dame in Lausanne? Would I have enough time given the above ones to cover.

5. How is the walk from Lausanne train station to Notre Dame? Would that give enough feel of Laussane?

6. Is there anything else I can see in the night?
Is it a good idea to wander the streets to Lausanne/Montreux/Vevey at night say until 9:00pm before returning to hotel in Montreux.

BTW, I have a very early train to catch the next day to Paris.

Thanks in advance.