I’m only a part time drummer, but I’ll take first shot at these.
1. What’s the deal with putting tape and pads on the drum head? Also, what’s with the pillow in the bass drum? Couldn’t the drums be manufactured in a way so that you didn’t need this?
In both cases of tape and pillows, it helps reduce ring.
Some snares have a pad inside which can be adjusted to reduce the ring as well, but most other drums don’t have this.
2. I’ve seen some right-handed drummers switch to a left-handed style in certain songs (that is, playing the snare with the right hand and the hi-hat with the left). Is this a common thing?
I haven’t really noticed this and I always play pretty straight forward, so I’ll let someone else answer this one.
3. Drum heads: clear vs. white - a difference in sound or personal preference?
Different drum heads make different sounds and react differently to how they’re played and with what (sticks, brushes, mallets, ect). Normally drummers have heads they prefer.
4. What makes one manufacturer better or worse than another?
For me, it is two things. Tone of the drums and the hardware on the drum. Cheap drum sets might sound ok but their hardware is one of the worse things about them. Stuff breaks, comes loose, etc. After you replace that stuff you might was well have bought a better set to begin with.
**5. How often do you need to tune the drums? **
I used to tune the set before each recording to have the drums mesh better in the song. Sometimes I’d want a crisper snare sound or a lower, more floppy tribal floor tom. As for other people, like live drummers,. I dunno. I’ve only played in studios.
6. Some drummers angle the hi-toms towards themselves, while others (eg. Clem Burke of Blondie) will set them horizontally. Again, is this just a preference or is this advantageous in any way?
I always had my toms at an angle for the ease of hitting them.
7. I see that the majority of drum kits are set up the same way. Are there any drummers with “odd” setups?
My old drummer had to hi hats. One in the regular place and the other over the floor tom. The foot petal for the “remote” hi hat was controled by a cable.
I think you’ll find most drummers have the basic 5 piece setup in the normal places but place their splashes and crashes as well as electronic pads in places that work best for them.
8. How many drums is too many? Neil Peart seems to have every type of drum there is. Is this just for show or does he (or any drummer) need that many things to hit? 
Personally, I think half of Pearts set is for show.
9. Gongs? I remember someone say (sarcastically, I’m sure) that if the drummer had a gong, you shouldn’t take the band seriously.
That sounds about right to me.