Should 3 takeoffs and landings to stay day current be solo? Let's assume  that I fly every weekend with a friend which is not a pilot. Can I log that time as PIC and count the takeoffs and landings toward the currency requirement as stated below: 


  Sec. 61.57: Except as provided in paragraph (e) of this section, no person may act
  as a pilot in command of an aircraft carrying passengers or of an
  aircraft certificated for more than one pilot flight crewmember unless
  that person has made at least three takeoffs and three landings within
  the preceding 90 days, and -- The person acted as the sole manipulator
  of the flight controls; and The required takeoffs and landings were
  performed in an aircraft of the same category, class, and type (if a
  type rating is required), and, if the aircraft to be flown is an
  airplane with a tailwheel, the takeoffs and landings must have been
  made to a full stop in an airplane with a tailwheel.


Does sole manipulator of the flight controls means solo and by yourself (alone) in the airplane such as Cessna-172 or does it mean you can have a non-pilot passengers?
Yes you can count that time as PIC and towards this currency requirement.

The regulation requires that you are the only one who moved the flight controls during takeoff and landing. This means you could fly with anyone else in the cockpit (including a flight instructor, another pilot, or non-pilot friends) but you alone must be the person who performs those takeoffs and landings in order to remain qualified.

This eliminates a few scenarios from counting towards the currency requirement, including:


You flew with another pilot, counted yourself as PIC (because you were more qualified or by prior arrangement) but didn’t actually do the work yourself
You flew with an instructor, and they helped you with the landings