You can omit "it" from the sentence "Yesterday it was one month since he got fired" and also "Today it has been one year since I've been here", but they both sound correct and it doesn't make much of a difference.
The tweet is correct if the person who tweeted it is talking about multiple songs, not just one song. Since the ranking of the songs belongs to the songs, then the apostrophe is correct, since it is possessive.
I hope this helped!