Yes, all of our SUP paddles float. With any 3-piece paddle you do have to be careful you don't submerge it repeatedly or it may slowly take on water and then once it gets waterlogged it can sink. You can prevent this by just opening it an pouring out the water in the shaft, but keep an eye on things if you or the kids are frequently submerging you paddle.
It is possible for any paddle to snap, but it's not common for paddles from reputable companies. The low-end aluminum adjustable paddles are notorious for this, so we recommend they only be used as travelers, not as an everyday paddle. Also, some of the off-brand, package deal carbon-fiber paddles are notorious for snapping. I had one snap the second day I used it, right at the joint between the blade and the shaft. It was just overall a bad joint design.
On the paddles we carry, the carbon kevlar ones are pretty much bulletproof. In a couple years of selling them, we've never had a report of one snapping. On our Tower Ultra-light carbon fiber paddles, we've only seen one snap ever and it was abused pretty bad for about a year in our demo fleet before it did. On the low-end, the inexpensive 3-piece fiberglass paddles are pretty solid, but they can.
The take away here is that it's smart to invest a little money in a decent paddle, for both performance and safety concerns. You never really want to have a paddle snap when you're out paddling by yourself.