1) no. As others have pointed out, Hieroglyphs in their pure form were supplanted in Egypt itself by other, derived forms of writing.
2) no. logographic writing works far, far better for Tibeto=Sinitic languages that aren't inflected. Indo-European and Semitic languages have too many declensions and conjugations and such for any logographic system to work. Even Japanese, which borrowed Chinese culture and writing pretty much whole had to invent an alternate system (hiragana, katakana) to supplement it enough for it to be practical.
3) no. Egypt never developed the cultural and political dominance to impose on others or cause others to adopt their culture and writing system.
1. True, but how much was because of the influence of the Semitic alphabet and especially in later eras the Phoenician and Greek alphabet? From my knowledge of Japanese, how different is that from the process which hiragana evolved? It seems like the main difference is that there already was a competing script to be used (the Semitic alphabets) compared to in East Asia where there as nothing to really do but alter Chinese characters and reappropriate them for certain purposes.
2. Exactly what I was going for. English or any other Indo-European language is not impossible to read using some hieroglyphics (or cuneiform as speculation here is) derived system. And there's always the potential for using a kana-like system to represent the endings and such.
3. Perhaps it could've been different? I have no clue how.
Syllabaries have not died out. Only one alphabet has been created that was not directly derived from Sinitic, and that was Hangul
At least two syllabaries have been created, the Cherokee and the Cree, also used by some Innuit. If it had not been for the former $20 bill person, the Cherokee could be much more used now
I've seen a theory that Hangul was inspired by Indian alphabets. I don't know how true that is, but I'd classify Hangul as a very logical script as syllabaries tend to be.
Cherokee doesn't really have a future, since as long as Europeans dominate them their language can't really end up being used much more than now. The Cherokee alphabet might even be a barrier to some degree.
There are also syllabaries like Vai, used in West Africa. And katakana and hiragana, of course.
Alphasyllabaries are even more common (Ethiopia, several Indian scripts derived from Brahmi).
There a case to be made for syllabic writing being generally the most intuitive, since it keeps reappearing historically, evolving from either logographic/morphemic scripts or abjads, or being invented independently (in the case of Cherokee, although with European inspiration).
Actually, most logographic scripts should be considered logosyllabic (including some stages of Chinese and cuneiform), and several alphabets are actually alphasyllabaries (note that both Hangul and Romanized Vietnamese use alphabetic writing to form graphically distinct syllabic blocks, as many Indian systems do).
Vai seems like it came from Cherokee, based on observations like Cherokee freedmen moving to Liberia and inspiring the Vai people. Not technically original, but still an innovation based on an innovation.
Syllabic writing is definitely the most sensical, based on my own experience in how easy I found Aboriginal syllabics to learn. It's simple logic, basically.