I'll do my best with these:
1) We don't know, but it took him several thousand years to hone them properly and reach his full potential.
2) When he was fully functional he could force entire armies to kneel before him, engage in psychic duels, grant immortality, heal both men and machines with a touch, stop time and change his appearance. In the 'present' of the 41st millenium (besides being almost dead), he's too busy powering the Astronomicon, a psychic beacon that makes warp travel possible, to do much of that, though he dabbles occasionally.
3) The Emperor is incredibly powerful in his own right: his genetic code is what makes up Primarchs and to a lesser extent the Astartes, so he's clearly abnormally powerful, and he may have mechanical enhancements we don't know about.
4) Depends: if this was before the Heresy, he'd probably manage just about, given none of them had developed psychic potential besides Magnus, who even so was far less powerful than the Emperor, not to mention that Emps is no slouch in combat. Post-Heresy... maybe, but Horus almost killed him (admittedly due to the Emperor being unable to kill his son out of love at one point) alone with chaotic enhancement, four of his sons are Daemons, and some like Lorgar and Magnus are psychic up the wazoo, so he might have issues (assuming he's not a corpse on a Throne).
5) Yes.
6) Yes, even if he didn't always so it. Even when Horus had fallen so far, he couldn't initially bring himself to kill him, and coming into conflict with his sons before the Heresy was always unpleasant for him.
7) He looks like a master of tens of thousands of years swinging a sword with the strength of a demi-god.
8) Typically a sword, which we think is called the Burning Blade.
9) We don't know, but he probably did.
10) He doesn't really have free time, he's either leading armies, making scientific advancements or honing his psychic powers. Now he's on the Throne, he projects the Astronomicon and that's about it.
11) Yes but not too often.
12) Ditto.
13) He would've delgated to sub-commanders and the like but in the end, even under the Primarchs, all roads led back to the Emperor.
14) Overwhelming physically, psychically and mentally: it sometimes hurt the Astartes' eyes to look at him, so imagine how mortals felt. As a person he was kind and benevolent, but not warm.
15) Probably, more because he had other shit to do than because of any moral code.
16) Ditto (not sure about Russ though, he's a bit strange like that)
17) He might've been able to teleport, but not naturally no: only Sanguinius could naturally fly.
18) The latter: abhumans and some xenos survive in the Imperium, but most of them get shown the business end of a boltgun pretty early in diplomatic situations.
19) Yes, as are all Astartes, assuming nothing interferes with that (like for example being stabbed through the gut by a daemonically-infused Primarch blessed by all the Chaos gods whilst simultaneously being filled with psychic bullets by the same son. Seriously, how the fuck is the Emperor still alive? Dude's insane)
Hope this helps!