Switzerland - 8-10 Days

You don't "need" a pass, just a ticket. Now there may be some advantages to a pass or Half Fare Card, mainly financial. They sell tickets at stations and vending machines and on-line to an app.

Where are you going after Lausanne? And how are you going?

"Do I need a Swiss travel Pass and Golden Pass?"

You don't "need" a Swiss Pass. You could just choose to purchase point to point tickets if you wish.

Golden Pass is the name of a particular train...not a travel pass.

You can look up train times and prices in Switzerland on the Swiss Railways website: https://www.sbb.ch/en/
The "from" price shown there assumes you have a Half Price discount Card (which most Swiss residents do). Either double that price, or click on it to see the other prices.
For example, Vevey to Rougemont costs CHF 26 full price, Zürich Flughafen (airport) to Vevey costs CHF 79, Vevey to Lausanne costs CHF 11.20.
If these are the only trips you will be taking by train, just buy normal tickets at the station on the day. If the total of your tickets exceeds CHF 240, you can buy a Half Price discount Card for CHF 120 (details here: https://www.sbb.ch/en/leisure-holidays/travel-in-switzerland/international-guests/swiss-halffare-card.html ) and save some money.

How will you get home? Do you need an extra train trip Lausanne to Zürich airport?

P.S. not sure what you mean by "metro rail".

What do you mean by "- 8-10"?

Are you saying sometime between August and October?

I do not know why you are flying in to Zurich. Why not fly in to and out of Geneva? Much less time-wasting. There is plenty to see in the Lake Geneva and Pays D'Enhaut area to keep you busy for all of your trip. Its also a shame not to spend a day in Geneva itself as it is lovely.

I live in the area so don't hesitate to ask for any more info. What time of year is your trip?

The OP does not reveal their home location, but there are few direct flights from North America to Geneva, but many to Zurich. This is the normal reason for flying into Zurich, and the one that I use.

what is a half price card?
If my calculations are correct, Zurich/Vevey $40, Vevey/Rougemont $50, Rougemont/Lausanne $55, Lausanne/Geneva $50
Total $195
Swiss Travel Pass (includes ferry, museums, etc.) $449/2nd class - $718/first class?
Please advise if I am correct.
Thank you
Louise

A Half Price Card is a discount card you can buy which allows you to only pay half fare (children's fare) for all transport in Switzerland.
It costs CHF 120 for 1 month. Details here: https://www.sbb.ch/en/leisure-holidays/travel-in-switzerland/international-guests/swiss-halffare-card.html
If your total transport costs in Switzerland exceed CHF 240, it would pay off to get a Half Fare Card.

You can look up fares on the SBB website: https://www.sbb.ch/en/

Your prices confuse me, because you use $. Switzerland uses the Frank (CHF), and that is what SBB prices are in. I have no idea what sort of '$' you mean or where you got these prices from.

I quoted you the prices for some of your trips in my previous post:
Vevey to Rougemont costs CHF 26 full price, Zürich Flughafen (airport) to Vevey costs CHF 79, Vevey to Lausanne costs CHF 11.20.
A Swiss Travel Pass costs (2nd class): 3 days CHF 225, 4 days CHF 270, 8 days CHF 398, 15 days CHF 485
Details here: https://www.sbb.ch/en/leisure-holidays/travel-in-switzerland/international-guests/swiss-travel-pass.html

P.S. Lausanne to Geneva takes 36 minutes and costs CHF 23 full fare, 2nd class (CHF 11.50 if you have a Half Price Card). All these prices are from the SBB website, and are what you pay when you buy at the station on the day. There are rarely discounts for advance purchase.