Achievements:
You can get achievements for doing certain tasks in single play and multiplay modes. These achievements count to your gamerscore for your gamercard.

Yes you can get achievements on LIVE.

There are 50 in all and will give you 1000 gamerscore points in all.
10 Kills in Killcount Get 10 kills in Killcount mode
10 Melee Kills Get 10 Melee kills in an Multiplayer mode
10 Kills in Team Killcount Get 10 kills in Team Killcount mode
Complete Single Agent Complete Single Player on Agent Difficulty
Complete Single Secret Agent Complete Single Player on Secret Agent Difficulty
Complete Single Perfect Agent Complete Single Player on Perfect Agent Difficulty
10 Explosive Kills Get 10 kills using explosive in any Multiplayer modes
10 Sniper Kills Get 10 Sniper kills in any Multiplayer modes
100 Kills in Killcount Get 100 kills in Killcount mode
10 Headshot Kills Get 10 Headshots kills in any Multiplayer mode
100 Sniper Kills Get 100 Sniper kills in any Multiplayer modes
Played 10 Deathmatch games Play 10 Deathmatch games
100 Explosive Kills Get 100 kills using explosive in any Multiplayer modes
10 Territories Held Score 10 points in Territory Gain mode
100 Kills in Team Killcount Get 100 kills in Team Killcount mode
100 Melee Kills Get 100 Melee kills in an Multiplayer mode
100 Headshot Kills Get 100 Headshots kills in any Multiplayer mode
10 Minutes Survived Survive 10 minutes in Onlsaught mode
Complete Single Dark Agent Complete Single Player on Dark Agent Difficulty
Complete Co-Op Agent Complete Co-Op on Agent Difficulty
Complete Co-Op Secret Agent Complete Co-Op on Secret Agent Difficulty
1 Solo Mission On Dark Agent Complete 1 Solo misson on Dark Agent Difficulty
5 Co-op Missions On Dark Agent 5 Co-Op missons on Dark Agent Difficulty
1 Co-op Mission On Dark Agent Complete 1 Co-Op misson on Dark Agent Difficulty
1000 Explosive Kills Get 1000 Explosive kills in any Multiplayer Mode
1000 Melee Kills Get 1000 Melee kills in any Multiplayer Mode
1000 Headshot Kills Get 1000 Headshot kills in any Multiplayer Mode
1000 Sniper Kills Get 1000 Sniper kills in any Multiplayer Mode
Completed Co-Op Perfect Agent Complete Co-Op on Perfect Agent Difficulty
Completed Co-Op Dark Agent Complete Co-Op on Dark Agent Difficulty
Played 100 Deathmatch Games Play 100 Deathmatch games
Played 1000 Deathmatch Games Play 1000 Deathmatch games
Played 10 Dark-Ops Games Play 10 Dark-Ops games
Played 100 Dark-Ops Games Play 100 Dark-Ops games
Played 1000 Dark-Ops Games Play 1000 Dark-Ops games
1000 Kills in Team Killcount Get 1000 Kills in Team Killcount Mode
1000 Kills in Killcount Get 1000 Kills in Killcount Mode
10 Flags Captured Capture 10 Flags in Capture The Flag mode
100 Flags Captured Capture 100 Flags in Capture The Flag mode
10 Player Infected Infect 10 Players in Infection mode
100 Player Infected Infect 100 Players in Infection mode
1000 Player Infected Infect 1000 Players in Infection mode
100 Territories Held Score 100 Points in Territorial Gains mode
10 Rounds Survived Survive 10 Rounds of Eradication mode
100 Rounds Survived Survive 100 Rounds of Eradication mode
1000 Rounds Survived Survive 1000 Rounds of Eradication mode
10,000 CR Property Destroyed Destroye 10K CR of property in Sabotage
100,000 CR Property Destroyed Destroye 100K CR of property in Sabotage
100 Minutes Survived Survive for 100 minutes Onslaught.
5 Solo Mission On Dark Agent Complete 5 Solo missons on Dark Agent Difficulty

Unlock weapons to bring into other missions:
In order to unlock a weapon, you need to start a level that has that weapon in it, find that weapon, and finish the level with it. Simulations such as the level 0 are an exception; you don"t get to keep the weapons, because they are not real

The following list is most unlockable weapons, the type of weapon, and the amount of carrying capacity that it takes up. In the second column is the mission that the weapon first appears in.

The viblade is in the room with all the laser tripwires, on a stand in the center
The M60 can be taken from a guard when you fail to get let in by the front gate guard

Oh, and sniper take up 3 inventory spaces, making them unwieldy, but the jackal and shockwave can be found in rooftops escape, and bridge assault respectively.
Magsec 4 (Pistol 1) Mansion Infiltration
Magnum (Pistol 1) Rooftops Escape
Falcon (Pistol 1) Nightclub Stakeout
Phychosis Gun (Pistol 1) Trinity Infiltration
M60 (Heavy 3) Mansion Infiltration
Plasma Rifle (Heavy 3) Temple Surveillance
Rocket Launcher (Heavy 3) Bridge Assult
DW-P5 (SMG 2) Nightclub Stakeout
UGL Liberator (SMG 2) Nightclub Stakeout
CMP-150 (SMG 2) Sewer Retrieval
RCP-90 (SMG 2) Jungle Storm
KSI-74 (Assault 2) Lab Rescue
FAC-16 (Assault 2) Trinity Escape (off dead ally)
SuperDragon (Assault 2) Outpost Rescue
Laptop (Assault 2) Trinity Infiltration
Viblade (Close Combat 1) Mansion Infiltration (red triplaser room)
DEF-12 Shotgun (Close Combat 2) Nightclub Stakeout
Combat Sheild (Sheild 1) Trinity Infiltraiton
Frag Grenade (Thrown 1*5) Nightclub Stakeout
Multi Mine (Thrown 1*5) Temple Surveillance
Hawk Boomerang (Thrown 1) Rooftops Escape

Unlock Dark Agent:
Beat the game on Perfect Agent mode.