Spock is Vulcan and Vulcans believe in logic over emotion, they are supposed to be pretty cold and "flat" as a species. Leonard Nimoy brought a weird sort of charm with him as Spock (though Spock is half human), but it's hard to say if the new dude playing Spock FAILS at it... or gets it dead right, given the circumstances. I also haven't seen the movie yet.
Holy shit I just looked up who is playing Chekhov in this because I realized you're right and I haven't seen him in any trailers or ads and it's THIS GUY:
http://en.wikipedia.org/wiki/Anton_Yelchin for one he's three years YOUNGER than me and it's the dude from that fucking Justin Timberlake movie about the drug dealer. What a weird choice. I know this is YOUNG KIRK and stuff but this guy is like 19 isn't he? He's also got a bit of a babbyface going. How weird!
Oh he really is Russian. Like Steel said though, Chekhov is sort of a outdated character, created very PROGRESSIVELY considering he was Russian and created in the midst of the Cold War but it doesn't mean nearly as much today.