similar thoughts, 15' is kind of arbitrary, but it's deep enough to be relatively easy to maintain buoyancy for new divers, and 15' is deep enough to keep you out of harms way for most boats.
The ascent rate should be more correctly stated as "no more than 30ft/min". The safety stops can also be completed if you are shore diving by meandering around at relatively shallow depths. These are again precautionary stops, not decompression stops, so if you have to blow it you can, though it doesn't hurt to hang out at that depth and play around for a few minutes. Good practice for mandatory deco stops if you get to that point later down the road.
If you are diving less than 30', you really aren't on-gassing enough to really off-gas enough at 15' to warrant the stop, if you're diving like 50+ then you want to make them, and the deep stop thing is starting to come out, but science isn't really behind it, so if you're diving square profiles to 80+ft, it doesn't hurt to ascent to 40', chill out for a minute, then ascent up to 15', and chill out for a few minutes. This is all within NDL's, and it's important during these stops to keep moving. Slow deliberate motions from your arms and legs help. You don't want to be actively moving so much as every once in a while make a stretching motion to keep the muscles moving to promote blood flow.