Nothing really happens to Ryuk. He goes back to his old boring place in the skies. He just did all that for fun, nothing less, nothing more. He never had any feelings involved. So, everything was still normal for him.
Ryuk first met L at the exam, and L never met Ryuk, since he did not touch Ryuk's notebooks.
There isn't really any indication of that.
He is a Shinigami and has no last name.
Well, if it's Kira from Death Note, then Ryuk, the shinigami Killed him
Yes. Because as Light is about to die, he asks Ryuk if the reason the Death Note says people who have used the notebook go to 'mu' (nothingness) is because there is no heaven or hell, and Ryuk says that is correct.
Ryuk
Ryuk first met L at the exam, and L never met Ryuk, since he did not touch Ryuk's notebooks.
Ryuk kills Light by writing his name in the Death Note.
umm... ryuk's Japanese name is ryuuku if that's what ur asking
Rem and Ryuk are Shinigami just as they are in the manga and anime series .
Ryuk-nang Ko has written: 'Han-Chung hochingo ui taejo yongu'
In Episode 24, Light gets the death note back and recovers his memories. He then kills Higuchi making the Death Note his again. But the original owner of the death note at that moment is Rem, so he has to touch the piece of paper from the Misa's notebook to be able to see Ryuk. Ryuk stays Misa's shinigami until Mello kidnaps Sayu, then Light temporally returns one of his notebooks to Ryuk, sends it to the police, and when Soichiro dies, Light is again the owner of one of Ryuk's notebooks.
He falls in love..
Ryuk Killed him in the last book
There isn't really any indication of that.
He is a Shinigami and has no last name.
In the series, it was never confirmed the last time that a shinigami had dropped their Death Note until Ryuk. If we are assuming that you are asking from this date, the last shinigami would be Ryuk.