Vaporetto Help to Murano, Burano and Torcello

Yes, you can go from one island to the the another by vaporetto. Torcello is very close to Burano. Don't go on a tour, totally unnecessary. Torcello is small with an historic church, interesting to see. We never looked at schedules, just go.

yes you can visit all 3 islands by vaporetti (plural). If there is one that takes you to all 3 islands, I don't know about it. I make that a day trip and spend some time on each island. Connections are frequent enough so you shouldn't feel rushed on any one island.
I highly recommend lunch on Burano. Of the three islands, Torcello is by far my favorite. Murano is just a necessary stop along the way.

Each time you get off the boat, is 1 trip. So for all 3 islands, and a return would be 4 trips.

If you're there for at least 2 days, look at these tourist cards. They're good for a full 24 hours.

https://quickvenice.com/transportation/actv-tourist-travel-cards.htm

We do this every time we are in Venice and using Fondament Nove is smart. We also buy a vaporetto pass each trip as we get a lot of use out them. At the very least a one day pass makes sense for this day trip. Doing it on your own means you can linger where you like. Rick Steves, in his guidebook, has a very nice self-touring plan for all three islands.

I would want much longer than 45 minutes since it takes about that much time just to get out to Burano. Torcello is a little further, Murano is closest to Venice. You have to check the schedule for times, the vaporetto is like a bus line in that you take different routes for different destinations. In Murano there are two different stops and you may have to switch to catch the line to Burano/Torcello.

http://actv.avmspa.it/en/content/orari-servizio-di-navigazione-0

This route map will show you how to connect the islands.

http://muoversi.venezia.it/sites/default/files/mappa_linee_di_navigazione_NOV_2018_WEB.PDF

Remember to tap in at the little machine before boarding the boat, even if you are using a pass.

I vote against the tour you mentioned.
Burano in 45 minutes will basically get you off the vaporetto, through the (typically) crowded vaporetto station and you'll barely see any of the town/island before you turn around and do all that in reverse to get back on the vaporetto.
That's not enough time.

I think I arrived on Burano around 10:30am or 11 and stayed past 5pm. And I will still go back the next time I'm in the Venetian Lagoon.

If you DO go without a tour, do a favor to yourself and get off one stop before Burano at Mazzorbo. It's a regular vaporetto stop, so less crowded, and there's a nice quiet, peaceful island with a vineyard to wander through before you walk across a pedestrian bridge to Burano.
While I highly suggest getting off at this stop and walking to Burano, I do not recommend the opposite when you're leaving. There was little room left on the vapretto leaving Burano, let alone room for anybody wanting to get on at the next stop.

Nancy, whenever in Venice, I have always enjoyed a day on these islands. No tour really necessary. Certainly a vaporetto pass, for your whole stay in Venice, or at least for one day, is a good idea. My guidance is to get an early start and allocate enough time on each island you mention. On Murano, I enjoyed taking a healthy walk beyond the commercialized area, out by San Donato Church. This is a lovely locals area, and on the way I found the gallery of a local glass makers co-op, where I bought a couple nice pieces of Murano glass, that I have on my windowsill and am looking at right now. I have never been to the Glass Museum, so can’t comment on that. Also, some of the commercial glass galleries have “private areas” with large, expensive, colorful, very beautiful and photogenic glass works; if you ask, you will probably be invited in, especially if you are without kids in tow. I think they mostly want to avoid crowds in there, especially young kids who are less than ruly. On Burano, you also want to go beyond the commercial area, and stroll through the pastel-colored residential neighborhoods and canals. There are several excellent mostly fish/seafood restaurants, I recommend the famous fish risotto, although often the menu says that is for a minimum of two people, sometimes I have talked myself into that dish for just me. Plead politely and with sad eyes. I have also not gone through the Lace Museum, so can’t comment there. Finally, Torcello is the birthplace of Venice, with an ancient church complex. Give yourself enough time on the island, about an hour. It takes 5 to 10 minutes to walk from the vaporetto to the church complex. The last time I was on Torcello there was only one kind of ticket to visit all three buildings at the complex, 9 or 10 or more euros as I remember, so give yourself enough time to justify the expense. Enjoy a wonderful day!

Agree with others, no need to take a tour. We enjoyed colorful Burano for a few hours in the early am. Had lunch there and headed to quiet Torcello. The church was the highlight.
We used the helpful audio guide. We were in Venice last September during the film festival.
We also took the Vaporetto to Lido and enjoyed a few hours by the beach. You might consider visiting San Giorgio Maggiore. You can enjoy the best panoramic views of Venice from the bell tower. This includes San Marco, Doge's Palace and the Grand Canal. Great photo opportunities. Enjoy your stay!

At the Lace Museum on Burano, I got to see a group of ladies making lace - very impressive.