Can Harry still understand Parseltongue?
Harry can no longer speak it
Harry being an accidental Horcrux meant he was bound to Voldemort in so many ways, just like Voldemort was bound to serpents. Not only could Harry speak the language of the snake, but could see through the eyes of Nagini, another of Voldemort's Horcruxes, as it turned out.
The ability to speak Parseltongue is usually inborn; a wizard is born being able to speak Parseltongue, and those who are not born with the ability cannot normally learn the language (although, according to the author, Dumbledore may have learned to understand it, and in Harry Potter and the Deathly Hallows, Ron learnt ...
Another notable Dark wizard who was also a Parselmouth was Herpo the Foul. However, as Albus Dumbledore pointed out, there were Parselmouths among the great and good as well, the most well-known of which was Harry Potter.
In other words, he gained the knowledge required to work as an Auror. By the time Ron opens the Chamber with Parseltongue, he has contained a fragment of Voldemort's soul, and he retains that memory. It has changed him permanently.
Known Parselmouths
Ginny Weasley was able to speak Parseltongue while she was possessed by Tom Riddle's Diary, which enabled her to open the Chamber of Secrets.
At King's Cross, meeting Dumbledore again, Harry's scar actually disappeared. He had wished it gone so many times.
Neither of them is Slytherin's heir. Although, as Dumbledore says, Harry's ability to speak Parseltongue is a skill accidentally transferred by Slytherin's actual heir, Voldemort, when he tried to kill Harry as a baby. So perhaps this is one myth with a bit of truth to it.
Harry Potter came very close to being sorted into Slytherin before he persuaded the Hat to sort him into Gryffindor. Yet the spectre of Slytherin haunted him for some time afterwards, becoming particularly potent in Harry Potter and the Chamber of Secrets, when he was rumoured to be the heir of Slytherin.
'Seethaaa-ssse-hathehhh-hathehhh-ayaeeh' means 'Hello'.
Salazar Slytherin and his descendants were fluent in Parseltongue — the ability to speak to serpents. In the series, Slytherins were often associated with snakes and serpentine imagery.
What did Harry say in Parseltongue to open the chamber?
Ron and Hermione re-enter the chamber in Harry's seventh year; knowing that Basilisk venom will destroy a Horcrux, and having a Horcrux they need to destroy, Ron, who has twice now heard Harry pronounce the word "open" in Parseltongue, opens the Chamber by imitating the sound of the word.
Behind the scenes. When Harry and Hermione are on the first floor of Bathilda's house, Nagini (inside the corpse of Bathilda) tells Harry to "Come!" from the next room in Parseltongue.
Warner Bros. has developed a Parseltongue translator – put in a message and it will be converted into Parseltongue!