Learn Italian: Il fatto che la bufala circola online è innegabile. - The fact that the hoax circulates online is undeniable.

The phrase il fatto che takes the indicative when it introduces an objective, concrete reality. Because the sentence explicitly states this fact is undeniable (è innegabile), the circulation of the hoax is presented as an absolute certainty, not a subjective opinion.

How would the verb change if the sentence were 'The fact that the hoax circulates online is annoying'?

You would need to use the subjunctive form circoli instead of the indicative circola. When il fatto che is followed by a subjective evaluation or emotional reaction (like finding something annoying), it triggers the subjunctive because you are focusing on your feeling about the event rather than just coldly asserting its existence.

Does bufala really mean hoax? I thought it meant buffalo.

Yes, while bufala literally means water buffalo (as in mozzarella di bufala), in modern Italian it is the standard colloquial word for a hoax, fake news, or an urban legend. It likely comes from an old regional expression about leading a gullible person by the nose like a buffalo.

Is the English loanword online considered an adjective or an adverb in this sentence?

It acts as an adverb here, directly modifying the verb circola to explain where the hoax circulates. Note that English loanwords like online are invariable in Italian anyway, meaning they never change to reflect gender or number.