have a walk or go for a walk

Say the second one. I don't think I've ever heard a native speaker say have a walk. Take a walk is also possible.

Note every day should be two words here.

Have a walk is possible, though it seems to be more common in BrE. There are 16 citations in the Corpus of Contemporary American English and 27 in the (smaller) British National Corpus.

I seem to learn something new about BrE every day.

Aspara GusI seem to learn something new about BrE every day.

Indeed. Stick around and eventually you'll even learn "have a lie-down", which is distinctly un-American.

CalifJim eventually you'll even learn "have a lie-down", which is distinctly un-American

The words or the action?

fivejedjonThe words or the action?

Hah! Good point. The words.

CJ

CalifJim The words.

That's a relief. I wouldn't like to think of an American caught napping being referred to the House Committee on Un-American Activities (HUAC).

fivejedjonbeing referred to the House Committee on Un-American Activities (HUAC).

To some of us that's the DHUAC, the D being for Dreaded.