"I want to meet them later."
Translation:Jeg vil møte dem senere.
Veeery late answer, but no, seinere is not nynorsk. "Senere" and "seinere" are both accepted forms of the word in bokmål, while "seinare" would be the nynorsk equivalent.
It depends on the context. The verb "å treffe" is maybe more a short meeting where you just say hi, while "å møte" might imply that you're talked a little bit longer. You will definitely be understood if you mix them, so you should not worry about that!
"Møte" as a noun is just like the word "meeting" in english. "Jeg har et møte med kollegaene mine" = "I have a meeting with my colleagues".
(Another fact about "å treffe" that might confuse you even more: "Å treffe" could in another context also mean "to hit" as in "Jeg treffer målet" = "I am hitting the target".)