"Peter does not laugh."
Translation:पीटर हँसता नहीं है।
Is "पीटर हँसते नहीं हैं" also OK? This is oblique in the sense of respect, is it accurate?
Not oblique (since you need a postposition for a noun/pronoun to go into the oblique, and verbs can't be described as oblique), but "हँसते... हैं" definitely acceptable as an "honorific plural" = singular 3rd person accorded plural verb agreement in order to confer a sense of respectfulness.
When a present habitual verb is negated, the form of "होना" can be dropped. Thus, "पीटर हँसता नहीं" should also be accepted.