The answer mostly has to do with the specific history of how the Romans acquired and adapted their alphabet, rather than with any particular features of Latin itself.
The Roman alphabet was derived from the Etruscan alphabet, which in turn was derived from the Greek alphabet (which in turn was derived from the Phoenician alphabet, but we don't really need to go that far back for our purposes). The answers to your first three questions all have to do with sounds which the Greek and/or Etruscan languages happened to lack, and which therefore weren't written in those alphabets.
- V stood for both the consonant [w] and the vowel [u]. Certain dialects of Greek had both those sounds and used different letters for them, Ϝ and Υ; Etruscan did the same. But when the Romans adopted the alphabet, they used Ϝ for the sound [f], and therefore had to use the other symbol (which they wrote as V) for both [w] and [u].
- I stood for both the consonant [j] and the vowel [i]. This goes back to the fact that Greek did not have the consonant [j], so when the Etruscans and later the Romans adopted the alphabet, they had to use the same symbol I for both sounds.
- C originally stood for both [k] and [g]. This is because Etruscan did not distinguish voiced from voiceless stops: it only had one velar stop, so only needed one letter. The Romans, who had two, eventually developed a new letter G so that they could make this distinction.
Your last question is a different issue, about sound changes in later Romance languages rather than about Latin itself. Most or all Latin vowels, not just E, underwent various changes in the various daughter languages.