That could be said for Naruto, not One Piece.
Nope, One Piece is first before Naruto, considering when both were released. Furthermore Naruto is more for kiddies.
Some cut? What cut?
Teenage Mutant Ninja Turtles? Haven't watch the current version of that series in which it didn't arrive here as it seemed but felt a bit of dissappointed of the characteristics of all the characters not only the cast (Probably when I played the TMNT.). Especially April O'Neill, supposedly a reporter but not. True, I too missed the old version.
Inuyasha is not quite but considering the succesion of Ranma in the past times, you can predict that it (Inuyasha) still attract the fans of Ranma.
OVA? Sometimes they are made good and some are not. Especially X-The Movie which I found out unsatisfied with the end. It has a series but I didn't have that one. Naturally I found out OVAs usually harmonized with the TV series more than being standalone.