Called a "track" on most devices (I think). It's a continuous recording. Very useful. Battery life on my phone seems fine when I use it. Keep phone in flight mode.
I don't think so, that's a pretty tall order.
It's easy to transfer from phone to Google Earth or other software. Haven't done it the other way myself, but imagine it would be fairly straightforward. I'll often find places of interest on satellite maps on PC and then manually mark them on my phone app. Sounds like a hassle, but for me, it's only usually one or two spots in a new location.
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