Learn Hardcore Japanese: netto de genin wo sirabeta ga, tyokusetu kiita hou ga hayakatta. - I looked up the cause on the internet, but asking directly was faster.

Because the fixed pattern is V-たほうが + (adjective/いい) to express preference or hindsight (“would be/would have been better/faster”). It does not literally mean the action happened.

General rule: ネットで調べるより、直接聞くほうが早い (neutral, general truth).
Hindsight about a specific case: …直接聞いたほうが早かった (“It would have been quicker to ask directly.”).

Does 聞いた here mean they actually asked, or that it would have been faster if they had asked?

In this construction it typically means the latter: “It would have been faster to ask (but I didn’t).” If you want to say you actually did ask and found it quicker, say something like:

結局、直接聞くのが一番早かった。
直接聞いたら早かった。

Why is が used between the clauses? Could I use けど?

Here が is a conjunctive “but/though,” not the subject marker. It’s slightly more formal/written than けど.

Casual: …調べたけど、…
More formal: …調べたが、…
Stronger “even though/contrary to expectation”: …調べたのに、…

Why is で used after ネット? Could I use に, を, or から?