Yes.

Regarding logging PIC time, 14 CFR § 61.51(e) states in part:

(1) A sport, recreational, private, commercial, or airline transport pilot may log pilot in command flight time for flights-

(i) Except when logging flight time under § 61.159(c), when the pilot is the sole manipulator of the controls of an aircraft for which the pilot is rated, or has sport pilot privileges for that category and class of aircraft, if the aircraft class rating is appropriate;

(ii) When the pilot is the sole occupant in the aircraft;

(iii) When the pilot, except for a holder of a sport or recreational pilot certificate, acts as pilot in command of an aircraft for which more than one pilot is required under the type certification of the aircraft or the regulations under which the flight is conducted; or

You really don't need to go any further than that.

You cannot "perform the duties" or "act as PIC" without a current medical certificate, (stated elsewhere in the regulations). The FAA breaks PIC duties out separately from "sole manipulator" and your friend must be that. But if you are a rated pilot flying the airplane you can log the time while you are sole manipulator.

Yes.

Regarding logging PIC time, 14 CFR § 61.51(e) states in part:

(1) A sport, recreational, private, commercial, or airline transport pilot may log pilot in command flight time for flights-

(i) Except when logging flight time under § 61.159(c), when the pilot is the sole manipulator of the controls of an aircraft for which the pilot is rated, or has sport pilot privileges for that category and class of aircraft, if the aircraft class rating is appropriate;

(ii) When the pilot is the sole occupant in the aircraft;

(iii) When the pilot, except for a holder of a sport or recreational pilot certificate, acts as pilot in command of an aircraft for which more than one pilot is required under the type certification of the aircraft or the regulations under which the flight is conducted; or

You really don't need to go any further than that.

You cannot "perform the duties" or "act as PIC" without a current medical certificate, which is stated clearly in 61.23(a)(3)(ii). The FAA breaks PIC duties out separately from "sole manipulator" and your friend must be act as PIC. However, if you are a rated pilot flying the airplane you can log the time while you are sole manipulator per 61.51(e)(i).