Learn Italian: Hai bisogno di un mutuo; inoltre, la banca chiede qualche documento. - You need a mortgage; moreover, the bank asks for some documents.

No, inoltre is neutral; it simply means "moreover" or "furthermore", adding another fact to the list. If you wanted to imply that the bank asking for documents is an extra burden or hassle on top of needing a mortgage, you would use an escalating connector like per di più or oltretutto.

Why is it qualche documento in the singular when the translation says "some documents"?

The adjective qualche (meaning "some" or "a few") is always followed by a singular noun in Italian, despite having a plural meaning. This is a common trap! If you wanted to use a plural noun, you would have to switch to alcuni, as in alcuni documenti.

Could I use domanda instead of chiede to mean the bank "asks for" documents?

No, chiedere is the correct verb when asking for an object to be given to you, like a physical document or a favor. domandare is generally used when asking a question to get information or a verbal answer.

Why is there a semicolon and a comma around inoltre?

Just like "moreover" in English, inoltre introduces a new independent clause that is related to the previous one. It is standard punctuation to place a semicolon (or a period) before it, and a comma immediately after it, to give the connector its proper rhetorical pause.