"You are walking."
How can you tell if it's singular or plural based off the English "you are walking?"
For that reason, both singular and plural translations are accepted, also both formal and informal.
And is Laufen irregular? I thought You plural would be Lauft?
Yes, laufen is slightly irregular -- it has umlaut for "you singular" and for "he, she, it".
But the verb form for "you plural" is indeed lauft, so ihr lauft is correct.
The Pearson editor who used ihr läuft in the accepted translations for this sentence made a mistake. You can report that if you want.
"running is rennen oder laufen and walking is gehen oder spatzieren " A German dictionary will confirm this
All right, let me check a German dictionary:
laufen can mean mean "gehen" (= walk; meaning 1b) or "zu Fuß gehen" (= walk; meaning 1c) in addition to "sich in aufrechter Haltung auf den Füßen in schnellerem Tempo so fortbewegen, dass sich jeweils schrittweise für einen kurzen Augenblick beide Sohlen vom Boden lösen" (= run; meaning 1a).
https://www.duden.de/suchen/dudenonline/spatzieren -- The word spatzieren is not found
spazieren (no -t-) means "gemächlich [ohne bestimmtes Ziel] gehen; schlendern" (roughly: stroll).
In my experience, it's (a) not used often on its own, and (b) is not exactly equivalent to "walk" when it is.
spazieren gehen, as a phrase, means "to go for a walk".
So I'm afraid that laufen is ambiguous in German -- though usage differs depending on where in Germany you're from. (Using it to mean simply "walk" is more common in the south than in the north.)
So I'm going to disagree with most of what you said, and certainly with the assertion that the distinction between the German words is exactly that between the English words "run" and "walk".