In grammar, the idea of modality is to express subjective attitudes and opinions of the speaker about a possibility, probability, necessity, obligation, permission, ability, desire, and contingency.
All these categories can be ranked by the degree from high to low, where must refers to the former and would — to the latter.
In other words, must asserts what we conclude to be the most likely interpretation of a situation or events, and would — a less likely one.
Cut to the chase, compared with would, must expresses a higher degree of probability and means "I'm sure", "I'm most certain", "most probably" whereas would means "I suppose/assume", "probably", "maybe", "I should think".
To refer to the past, we use would with the perfect infinitive:
A: I met a most beautiful girl at John's party yesterday.
B: Ah, yes! That would have been his cousine Ann.
P.S. Should you want to have modal verbs listed by their modality strength approximately, here you are:
High modality: must, ought to, shall, has to;
Medium modality: will, should, can, need to;
Low modality: may, might, could, would.
You should bear in mind that the idea of modality can also be expressed through nouns, adjectives and adverbs:
Modal nouns: possibility, probability, certainty, obligation,
necessity, requirement;
Modal adjectives: possible, probable, obligatory, necessary,
required, determined, likely, certain;
Modal adverbs: possibly, probably, maybe, perhaps, sometimes, always,
never, certainly, definitely.
I agree with those in the comments, that using "What [were you]/[have you been] doing?" is much more likely to be interpreted by the recipient as rude, or at least intrusive. I can't think of a situation in which I would use either of these phrases unless I was essentially accusing someone of doing something they shouldn't have been.
If I'm interested in what someone has been doing, instead of saying "What were you doing last week?", I might say "What did you get up to last week?", although if the last time I spoke to them was much more than a week ago and there's no specific reason why last week was important, then I'd probably just say "What have you been up to?".
Disclaimer: I'm a native UK English speaker, so some of the above might be a little regional to the UK. I have spent a fair bit of time in the US and understand a decent amount of their regional variations, but I'll let a native US English speaker fill in the gaps if necessary.
Best Answer
Yes, "taking too long" and variations like "taking a while" and "taking a bit" are common expressions in English.
"Can the phrase above be used?" or "Can the phrase above be of use?"