How to buy train tickets and Swiss Rail Pass vs Euro Pass

I think day 4-7 you mean Luzern, not Interlaken (Ost).

Most of the itineraries I see are 3 changes between Como S. Giovanni. Lugano, Luzern, Interlaken Ost. Lugano is 4 minutes, but this should not be a problem if you are ready to get off the train as it arrives in Lugano. walk down the ramp, cross to the other platform and up the ramp to your new platform. 2 minutes max.

At Interlaken Ost, you will have to hustle, but very doable, and if you miss it, you just wait 30 minutes for the next train. None of your trains require reservations, with the exception if you decide on the EC train from Como, then you need a reservation until the next stop 5 minutes later in Switzerland.

The Swiss Travel Pass is only valid to Grindelwald. You get a 25% discount from Grindelwald to Jungfraujoch and back. For the Schilthorn, take the train to Zweisluetschinen, change to train to Lauterbrunnen, then the bus to Stechelberg. then cable car to Gimmelwald, then Muerren. Your pass is valid to that point, then you get a 50% discount on the ticket the rest of the way up and back. Similar going to Titlis, your pass is good to Engelberg, then you pay reduced price to go up.
BTW, instead of Pilatus, the Swiss Travel Pass is valid to the top of Mt Rigi.

Your 8th day of the STP will get you from Zurich to the airport on the train. No Uber or taxi necessary.

Thee only other thing you have to pay for is the short train ride from Como to Chiasso for 1.60 CHF on the RE 80 train.

The Zurich airport is very accessible by train. The train station is in the airport.
Perhaps the Half Fare card would work best for you?
Enjoy this beautiful country!

Visit the Man in Seat 61 for help understanding train tickets

Is there any train mentioned that would also not be covered by a global pass?

Grindelwald to Jungfraujoch is only covered 25%. Grindelwald to Schilthorn is only covered at 50% above Muerren, and you must go to Muerren via Zweiluetschinen. You will need a seat reservation for the EC train from Como S. Giovanni.

Interlaken to Titlis is only covered to Engelberg, then discount to Titlis. Interlaken to Pilatus is only covered to Alpnachstad or Kriens, then discount to the top.

Thank you, everyone, for the valuable information provided. Now, my question pertains to the purchase of a half Swiss pass (SBB):

1) Since we are going to a trip in July, do we need to reserve tickets for long-distance train; Bernini Express in advance, perhaps in May/June? I heard train tickets are never sold out but long distance scenery needs to be booked in advance?
2) Do we also need to buy tickets to go those mountains; Jungfraujoch, Schilthorn, Titlis, and Pilatus?

3) If we buy a half Swiss pass, will a half Swiss pass offer the same discounts, such as 25% off at Jungfraujoch and 50% off at Pilatus, as full Swiss pass?

3) Lake Lucerne area, I am still thinking Mt. Titlis is must but next must will be Mt. Pilatus or other recommendation?

Thank you!!!

To travel on public transit you need a ticket, and tickets are for a route, and indeed never sell out. This is mass transit, and the public transport companies don't know, nor care, which particular service you are going to use the ticket on. This also means that you can take a different train than originally planned at your own discretion, that you can have breaks, and do not need to worry about short connections.
Also because public transit is fully integrated you usually only need one ticket, no matter how many different services (or even companies) involved.

But it is indeed possible that more people board a train/tram/bus than there are seats, and then some people have to stand. On long distance trains that is rare however.

On long distance IC trains you can also get a seat reservation. That guarantees you a seat. The only route I would do that on is the Gotthard route during summer. Reservations are also compulsory on the Glacier Express, and the Panoramic cars on the Bernina Express (but you can still travel in the normal cars with just a ticket).

That "ticket" and "reservation" are separate things is something that people unfamiliar with European train travel sometimes have issues with. But that is how it is.

With the Swiss Travel Pass (STP) you do not need tickets for any public transport, and you can buy discounted tickets for mountain transport. With the Swiss Half Fare Card (HFC) you will need to buy tickets for each trip, and will also get discounted tickets for mountain transports. The interesting thing here is that the STP only gives you 25% off on the Jungfraujoch trip, but the HFC gives you 50%...