I'm going to keep this to names only in the interest of minimizing spoilers.
Key
#: Only availiable as a continued romance if initiated in Mass Effect 2
^: Same Sex Romance option
%: Not a Squad Member
$: Does not count towards 'Paramour' achievement
All listed relationships except for Diana Allers count for Paramour.
Male Shepard
Ashley
Liara
Tali #
Miranda #%
Steve Cortez ^%
Kaidan ^
Jack #%
Diana Allers %$
Female Shepard
Kaidan
Liara ^
Garrus #
Samantha Traynor ^%
Diana Allers ^%$
Every Mass Effect 2 save file has a "QuestCompletion" variable that can be one of three values. Gibbed's save editor has dubbed these, "Quest Incomplete", "Lived To Fight Again", and "Went Out in a Blaze of Glory".
There is no "mission complete" save generated by ME2 like there is in ME1. Instead, every save file has this variable in one of the three states. Presumably, only saves where Shepard "Lived to Fight Again" will be viable to import, as Bioware has previously stated dead Commander Shephards won't be importable into ME3. (And obviously, you can't import without beating the game).
(Related: https://gaming.stackexchange.com/a/52493/336)
When importing into Mass Effect 3, you get to pick the actual save to import (i.e., quick, auto, or manual). Your save is always current, so there should be no worry about keeping your save "updated", other than simply saving normally from playing the game.
Best Answer
No, the grab animations vary from race to race. Quarian, Turian, and Human have a similar animation. Asari and Drell has a biotic flair and Krogan simply punches the enemy. This is shown in this YouTube video: