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Six words put I first and P third, and five of them open with IM. The pattern is almost entirely one prefix.
IMPLY and INPUT are the only words here in ordinary use. IMPED, IMPEL, IMPIS and IMPOT are real entries but none is something you would reach for, so in practice the page is a choice between two.
If the second letter is N the answer is INPUT, because it is the only word here that takes one. If it is M you are in the larger branch and the ending has to decide.
INPUT is the safer opening because the N branch holds exactly one word. Confirming or ruling out that single letter settles one entry immediately and points you at the rest.
E leads the fourth box on two words, which covers IMPED and IMPEL, the likeliest of the obscure entries once the common pair is ruled out.
Yes, comfortably. INPUT is the only other one in general use, and everything else on the page is a dictionary entry.
School slang for an imposition, meaning a punishment exercise. Word game dictionaries list it.
IM is a productive English prefix and a P follows it naturally. That single fact accounts for five of the six words here.