Birth star and Pada for every graha, from the Moon's longitude.
R = retrograde
Your birth Nakshatra is the lunar mansion the Moon occupied at the moment of birth — one of 27 stars spanning 13°20' each, further divided into 4 padas of 3°20'. It anchors the Vimśottari Daśā sequence and is one of the eight factors compared in Porutham matching.
A Nakshatra is one of 27 segments the sidereal zodiac is divided into, each 13°20′ wide. Your birth star is the Nakshatra the Moon occupied at the moment of birth.
Each Nakshatra is divided into four quarters called Padas, of 3°20′ each. That makes 108 Padas in the full circle, and the Pada is what maps a Nakshatra position onto the Navāṁśa chart.
Yes. The calculator reports the Nakshatra and Pada for all nine grahas, not only the Moon, since each sits somewhere in the same 27-fold division.