I also wonder why "If so, what?" is incorrect...

Colloquial English might say "if so, what then?" or "If so, then?" It does not always imply "what comes next," but simply "what is the situation?" and could easily include the idea of "how." It is closely related to the idiom "So what?" (How does it matter?) and is similar to the French usage "Comment ça?" or just "Comment?" (What did you say?)

It is correct, as SourireCache points out, that "comment" is not equivalent to "quoi"; and as Bennemann says, there is a difference in the meaning of the two words in English; but without context, the given translation is not the only possibility.

They're two different vowel sounds. Si and il share a vowel sound. Pronoun/noun is irrelevant as "Si elle" wouldn't get contracted.

It is actually explained at the lesson's tips and notes section. "Usually, only one-syllable words ending in E can be elided, but elle, si, and words ending in que also elide. However, si only elides before il and ils, so you must write s'il, but cannot write s'elle."

Plenty of them. Imagine you're in a meeting, and the boss says : "We have to know if the sales can be improved, and if yes, how ?" = "Nous devons savoir si les ventes peuvent être améliorées, et si oui, comment ?"

If it helps you with context, "If so, how?" is an acceptable translation. THat may be a more familiar phrase to you.

"Si" can mean "yes" if used as a response to a negative statement, like for example "Il ne peut pas le faire." "Si, il peut le faire." ("He can't do it." "Yes, he can do it.")

Yes, "si" can mean both "yes" and "if" depending on context. In this case it's the latter.