1 No reason, probably. It's the same variation as des/desu. Some silent vovels are really unpopular though, like "k(u)suri", which I never heard anounciated. Perhaps the character's sense of rhythm required it.

2 It's not actually used by the Emperor - who has a completely different set of words to use to refer to himself. You'll hear them actually used by royalty figures every so often.

It's more of a case where an older usage persisted among a better-educated class and thus became a status signifier after the fact. Definitely does have the connotation that you noted though, that the speaker had an upper-class education.

3 Actually, what reminded me of this was listening to Gruier in Mouretsu Pirates.

4 "Watakushi" is the original pronunciation of the word. That's rather hard to pronounce so it naturally got truncated over time with the original pronunciation reserved for people who need to be really, really formal.

The Emperor rarely needs to be really, really formal since he outranks everyone he speaks to. If he spoke to you it would probably be in plain speech.

The generally rule about which characters can be unvoiced seems to be "shi, chi and any non-compound -u character." So you typically hear "Watash'-tachi", "Watak'sh'-tachi" or "Watakush'-tachi" depending on how fast the speaker is talking.

5 "If he spoke to you it would probably be in plain speech."

On second thought I take that back. Assuming that you are not Japanese the Emperor would probably choose a formal but not obsequious level of speech. Uchi/sota (in-group/out-group) distinctions usually override distinctions in rank. The dignity of the Japanese nation would probably require addressing a foreigner formally.

6 As a practical matter I didn't think any foreigner could get close to the Emperor, unless it's a head of state or some equally important dignitary. Joe Slob Tourist ain't gonna get within a mile of Him.