1. Grammar and punctuation are correct. However, the sentence doesn't really make logical sense. Yes, it's okay (and generally preferred) to omit restating the subject in the second clause. Since the second clause is not independent, the comma is optional. I would personally put it there. Others may not.
2. "It is coming within two weeks' time." Note the differences. No comma, omit the word soon (it's unnecessary and subjective), and an apostrophe after weeks to denote its possessive nature in this context.
3. Remove from, as you stated, and this sentence is okay. The comma is indeed necessary here.
4. The bold phrase would probably be better set off by the use of em dashes rather than commas. Otherwise, it's okay.
5. In informal written English, yes, both sentences are fine as written.