I recently did the same thing - updated my mother’s phone. She moved from one of our older plans to our new plan and since she uses just a little data, she was surprised to see her monthly bill ($25 plus tax) go down (now $20 plus tax).
Yes. You can subscribe to the $15 plan with no data, and add data, $5 at a time, when you need it.
Data does not roll over. It expires at the end of the billing cycle.
That it expires can feel a bit frustrating at times. For example, my daughter sometimes runs short just a few days before the next bill is due. It seems like a waste to buy her another GB when I know she won’t use even half of it but I have to remind myself to step back and look at the total annual cost. I moved my daughter from our $25 a month plan, and most months she is fine with just one GB of data at $20 a month. So even if I have to add that additional $5 of data three or four months out of the year (and even if she uses just a bit of it), I’ve saved money overall.