When can a pilot share expenses with a passenger?

The types of expenses that can be shared are expressly stated in § 61.113(c) which are “fuel, oil, airport expenditures, or rental fees.” It’s also a requirement that the pilot not “pay less than the pro rata share.
Traffic Pattern Legs

FAA updates Advisory Circular for non-towered airport operations

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The AC notes that when entering the traffic pattern at an airport without an operating control tower, inbound pilots are expected to observe other aircraft already in the pattern and to conform to the traffic pattern in use. If there are no other aircraft present, the pilot should check traffic indicators.