No reservation are needed in Switzerland unless you travel in the panoramic coaches in the scenic trains.

If the train from Zermatt says "PE" then it's the Panorama Express with only panoramic coaches that need reservation. 

Thanks so much for the quick reply. I figured that about swiss trains but wasn't sure about one going into Italy. So in your opinion.. this notice is not something to worry about?

You can take the train from Visp to Domodossola without reservation as long as you don't travel further than Domodossola. It's an EC train but they are reservation free within Switzerland and until Domodossola.

Nice that you will travel on the Centovalli Bahn. You know that you need to follow the signs to Domodossola FART to find the little train that will take you to Locarno.

Ah! The "it's fine until Domodossola but not after" was the key piece I was missing. Thanks so much for this information.

While I have you, I'm guessing 5 minutes won't be enough time to change at Locarno from the FART to the regioexpress there and that I best look for the next train, right?

Officially from FART to main line it's 4 minutes. Normally the tightest connection has 6 minutes to change and this works. 

But Locarno and it's lake is also a nice spot to do a break.

According to the planners, 4 minutes is the minimum connection time in Locarno between FART and SBB/FFS, so it should be possible. But it doesn't hurt to have a plan B.