Pilatus

Mt. Pilatus is very easy to do on your own. You can just show up. You can make a very enjoyable circuit from Luzern called the Golden Route. I don't know the Swiss Travel Pass covers all the modes of transportation or not, but it will at least give a discount. You may want to explore that further.
"An alternative way to get to Mount Pilatus from Lucerne is to take the famous Golden Round Trip. This is a type of all-inclusive ticket that covers four different means of transport.

The first leg is a 15-minute bus trip from Lucerne to Kriens, from where you’ll take the cable car to Mt Pilatus. For the return trip from Mt. Pilatus to Lucerne, you will later ascend via the cogwheel railway to Alpnachstad. From there a boat will transport you back to Lucerne via the lake.

The Mount Pilatus Golden Round Trip can also be done in reverse, travelling first by boat then by cogwheel train, cable car and bus. "

I took this trip and thoroughly enjoyed it. I didn't have a travel pass so I just purchased a "golden ticket" from the front desk of my hotel.

We went to Mt Pilatus last September. If I remember correctly, the Swiss Travel Pass covers the train or boat part of the trip, and also the bus portion of the trip between Luzern and Kriens. With your STP, the cogwheel as well as the cable car portions are discounted. We purchased our tickets at the TI at the train station; others have mentioned buying tickets at the hotel. We didn't know hotels sold tickets to Pilatus.
We bought our tickets the morning of our trip because we weren't sure of the weather. I would purchase tickets either the day before or the day of your trip. We loved Pilatus, and the view of the surrounding mountains. We also saw several ibex.
Toboggan at the Pilatus Seilpark: You'd probably want to stop on your way down from Pilatus, via the cable car.
Furigen: Haven't been there.

Given the fact that you want to do the toboggan, I'd suggest taking the boat from Lucerne and then the Pilatusbahn cogwheel train to Pilatus. Stop at the top for lunch and then take the cable car down to Fräkmüntegg to the tobaggan. The first segment of the cable car uses a larger cabin, while the section from Fräkmüntegg to Kriens uses smaller telecabines. When you arrive at the bottom cable car station in Kriens, you'll have a short downhill walk to the bus station for the ride back to Lucerne (it's only about a 15 minute ride).

There's a Tourist Information office in the Lucerne rail station. I vaguely recall that it's one floor down from street level. They will be able to tell you whether your Swiss Pass will suffice for the entire trip.

You didn't say when your trip was taking place? This may or may not affect your plans....

• Alpnachstad–Pilatus Kulm–Alpnachstad (the cogwheel railway is currently closed) Important: The cogwheel railway runs from 26 May 2022 until 20 November 2022. The boat service between Lucerne and Alpnachstad will end on 17.10.2022.
• Kriens–Fräkmüntegg–Pilatus Kulm–Fräkmüntegg–Kriens Important: The facilities are closed due to maintenance work from 24 October 2022 – 4 November 2022.

Here's the full schedule - https://www.pilatus.ch/en/inform/timetable .

Oh gee! We are there May 20th. So is there a way to go without the cogwheel train?

All of the information you seek can be found here:
https://www.pilatus.ch/en/
There's a Pilatus shop located at Hirschenplatz 10, 6004 Luzern. It's in the center of town, you can buy tickets there and they have friendly staff to help you select the tickets you need. You can make it up without the cogwheel, you will just go up and down the same way (on the cableways). I hope you have a great trip up!

Yes, you can travel to Pilatus without taking the Cogwheel train, although it seems a shame to miss one of the oldest and steepest cogwheel systems in Europe. As the previous reply mentioned, you can take the two segment cable cars both ways from Kriens.

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One comment on the TI in the Lucerne: train station: it's on the track/street level (furthest over, on track 2 as I recall) up the platform from the Burger King. We were just there in July; the RS guidebook says it's by track 10 -- not.

Right, RS has many mistakes in his guide books.

The tourist office is located at platform 3, next to Burger King restaurant. It has always been there.

Things change. Not necessarily a "mistake".