I used to judge an HDD's lifespan by its power-on time.
No,you cannot predict an HDD’s lifespan depending on the power-on time.
But someone says new HDD will keep power-on but not spinning when it's idle. Is this true?
Yes,It is true as they are programmed to run in idle /non-spinning state when not in use but they are still powered on so that they can be ready to use when required.This also helps in power saving thereby helping with just a tiny bit of battery life as well.
Also, I find the power-on time increases as long as my laptop is on, though I did have the "shut down the hard disk after 20 minutes" setting in win10.
Power-on time is bound to increase as it is still in non-spinning/idle state so it needs some power to be ready for use.(HDD’s take a small amount of time to start up from a switched off mode,so it is better to keep it super low on power to save time,doing the same is power efficient as well)Windows is doing it’s job correctly as it is “shutting it down” by putting it into idle state when not in use(read the settings properly,it says only when not used for 20 minutes). You can’t shutdown a drive completely unless you have don’t have your windows installed in it because then windows would shutdown as well.
BTW, how can I tell if an HDD is spinning or not besides listening with my ears (no HDD light, of course)?
In laptops,the HDD is located beside the trackpad(usually) so you can feel the heat/vibration but if you want to be sure that it is in idle state/not spinning you could open task manager and in the performance tab you can select the hard disk graph and see the data given below,if you see that there is 0kbps read/write or anything less than 1kbps or if you see the active time less than 2%,you can say that it is not spinning.