Is use of "shall" archaic?

A friend of mine, pursuing BA(Hons) in English corrected me that no one uses shall now and often it is advised to prefer the use of should, would, etc.

Although Downton Abbey is set upon a time period decades ago, the characters make use of "shall" frequently in their sentences, I have noticed in some British movies and shows that the character make use of "shall" quite often. I couldn't help but notice that I never came across and American character making use of "shall" in an American TV show or movie, or maybe I missed catching the character making use of it.

What is with "shall" in this present-day? Is it obsolete now? Was it only used until contemporary era?

Solution 1:

shall, verb –Google

(in the first person) expressing the future tense. "this time next week I shall [(will)] be in Scotland"

Personally, I shall allow shall to become archaic only over my dead body. It's not that I shouldn't or that I won't; I will.

The only time it replaces should is in the idiom "shall I..."

Admiral Piett: "Shall I hold them?"

Lord Vader: "No. Leave them to me."

I can't think of any instance where it should replace would.

Solution 2:

In my (BrE*) speech "shall" is very much alive. In normal speech I say "I'll", but if I have reason to expand it, I'm as likely to say "I shall go" as "I will go".

And in a question, "Shall I" is much more natural than "Will I": I would say "will I" only when asking about a prediction or whether I will have permission or ability to do something in the future.

*Actually, this is one place where "British English" is an inadequate term, because Scottish English is different: many Scottish people do not use "shall" at all, even in permission questions: "Will I open the window?"