May I know..

The question is "may I know...?" and the rest is an indirect question, so (1) flows better. In conversation you might well use (2), but it's not a single sentence.

Yes, I want to add my voice to this.

May I know whether... is a somewhat formal way to begin a question. (There are differences between "whether" and "if" which you can find by searching for those terms here. Although in conversation, "if" is used for "whether" extremely often, if you are going to be so formal as to start "May I know" then you should probably use the more correct

Thanks for your replies. Is there a way to explain that 1) is a sentence, while 2) is actually two sentences, in grammatical terms?

1) May I know if the auto-backup feature work for these PCs?
2) May I know does the auto-backup feature work for these PCs?

#1 has a main clause with a dependent clause introduced by the subordinating conjunction if.
#2 has one clause with two finite verbs unsegregated by a conjunction or appropriate punctuation.

Mister Micawber#2 has one clause with two finite verbs unsegregated by a conjunction or appropriate punctuation.

What is a finite verb? Are the two finite verbs 'know' and 'work'?

I don't quite understand: "unsegregated by a conjunction or appropriate punctuation". Could you give an example that would make #2 correct?

Yes, Clarence: may...know and does...work. Both are finite, and a single clause or simple sentence cannot have two of them unless there is some sort of segregation (separation) of them by ( 1 ) coordination or ( 2 ) subordination or ( 3 ) punctuation:

1-- Does the feature work, and may I know this?
2-- May I kn

Thank you, Mister Micawber. That was very clear.

Mister MicawberThese all make your #2 structurally correct, but they are not necessarily very good ways to say it. If I were composing, I might use:

Could you tell me if the feature works?

I was thinking about the two sentences when drafting an email. Maybe I was trying to avoid t

"Is this feature active?"

"Does this feature work?" (see my post above)

Or: "I'd like to know whether ...", no question mark at the end.

Thank you for the suggestions!