They remove the roof trim and hide it behind there - one of the reasons I don't want to self-install is I don't want to make a mess of it (and these guys have done quite a few with good feedback).
Yes, parking mode requires it to be connected to the fuse box / hardwired.
Most the cameras have two modes in "parking" mode:
1 - 1 frame per second, constantly (most energy drain)
2 - Motion activated (minor drain to power the g-sensor, then turns on to catch the seconds after / perpetrator driving off).
So if you're leaving it stood for long periods, or prefer option 1, you need / it is recommended you get the battery.
Option 2 is fine without it, within reason (but you should add a battery voltage check to your normal maintenance routine if you've got any dash cam installed at all).
Regards the memory card, the dash cams seem quite erratic in this regard, a lot of people say card A does work, a lot say the opposite.
They are regarded as a "consumable" in dash cam use so you'll need a spare, for sure. I've bought a 128gb Samsung Evo to test in the thinkware, will advise as to success when I get it working.