Employer has 3 employees. 1 part-time NHCE, 2 HCEs. NHCE works less than 500 hours per year. Does this plan pass coverage? Is the NHCE counted for purposes of the 410(B)(6)(F)?

assuming that the NHCE never had 1000 hours and the plan has a 1 year wait for eligibility, then the plan passes since no NHCE are eligible.
If the plan has with immediate eligibility, then the person has entered the plan. If there was an hours requirement to receive a profit sharing then chances are you pass coverage because such a plan would be top-heavy, and the part timer would receive a contribution. but then you might fail 401(a)(4) testing.
(all this assumes of course you are not excluding part timers by definition, which of course you are not allowed to do)

Eligibility is 2 years and 1,000 hours. Does that mean that for 410(B)(6)(F) "employees" means those not excluded by statutory exclusions?

yes, though
I suppose you check 3d on the schedule T, because 100% of the nonexcludable NHCEs benefitted.3a says the employer employs only HCEs, which really isn't true.