In an informal setting, « Quand même » can be used to “punctuate” a conversation, a bit like “Really!”, or “Really?” in a way.

So, I would say that:

Quand même !

would be an equivalent to “Really!”

and

Quand même ?

an equivalent to “Really?”.

When used in a more formal way, inside a sentence, it would mean “even so”, “all the same” or “anyway” as you said in your question. In the case of your example:

Tu peux le faire quand même.

means

You can do it anyway.

in the context of something that would seem to be impossible or forbidden.

When used as an exclamation, quand même simply expresses surprise.

Un Monégasque sur trois est millionaire.
Ah, quand même !

The question form is similar to the interjection, and means something like “really?!”

Quand même can also mean “still” or “anyway” :

Je n’aime pas trop le rock, mais j’aime quand même les Beatles.

It’s also a mid-sentence interjection used for emphasis : C’est difficile, quand même, le français means almost the same thing as C’est difficile, le français, but the first may have a slight nuance that the speaker doesn’t necessarily expect the listener to know that French is difficult.

If you hear it many time a day from the same person, it may simple be a habit of language.

A sound exclamation point. Something like the “Tu m’en diras tant” of my grand-father, the “J’y crois pas” of my daughter, or the “Fan de pied” of my friend from Marseilles. All of them syntactically incorrect on purpose.

In facts, consider you as lucky! Your circle could use the more colloquial “Putain!” n times a day.

My understanding is that it means ‘None the less’ or ‘in any case’, try substituting this into the phrases above and you’ll see what I mean.