He could be a Halfmoon (HM), Over Halfmoon (OHM) or a Delta (DeT). Unless a Betta is at full flare it is difficult to distinguish the fine points which separate the three.
A Halfmoon has a perfect D-shape from anal fin to dorsal. Caudal has a 180 degree spread.
Over Halfmoon is just that...an exaggerated HM with more than a 180 degree spread.
The caudal of the Delta and Super Delta do not reach 180 degrees.
Here is the Forum's tutorial on fish-in cycling. A cycled tank means there is nitrifying bacteria established which keeps the aquarium water safe for the fish.
Take lots of photos of Parkey! He looks to be a marble or have the marble gene and what he is today may not be what he is next month.