Question #1 - When specifying an inline style in an HTML element, is it necessary to include a trailing semi-colon? For example ...
Q1: No, but I always include a trailing semicolon. Some years ago that semicolon could be a reason to a wrong render (or lack of) by some browsers. I guess nowadays is not a problem.
Q2: No, both ways means the same. Your election to include an space after the colon should be based on personal preferences for legibility.