Adjusting the "Time" setting will usually give you more mission area spawn points to hit, often (but not always) giving you more hostiles to encounter, which means more XP.

As for critical missions, you'll get more of the crit pack that comes out with each sub-chapter depending on your organization rep level. I think you get the first crit at 20 rep, and all five at 40 rep, but I'm not sure.

Archive missions are not dependent on org rep. You can run any of the sub-chapters at any rep level and it won't affect it.

Well, I just hit level 9, and I have run out of critical missions and now am able to choose my mission type.  My first question involves the "Time" setting: what does it affect?  Is it how long the mission will take to complete? 

My second question is about Archive Missions.  Will I experience all of my factions Archive Missions just by playing the Critical Missions that pop up, or are they two entirely different things?  I ask because I purchased the 1.1.1 ticket, and I swear I already did the mission it gives me!

Sorry if none of these questions make any sense... feel free to smack me around and yell at me until they do.

First off, welcome to The Matrix. 

Basically, the time setting is broken.  I always set it to the lowest setting (tiny), but that's more habit than anything else.  Contrary to what would make sense, there is a "sweet spot" in how long it should take you to do a mission... take too long to do the mish, and you get docked XP.  Do the mission too quickly and you get docked XP.  Generally if you kill every enemy you're given to kill (outside of extras that are triggered by alarms) you'll get the most XP per mission. 

The archives cover the entire story from the beginning.  The criticals you see pop up in your mission menu (after you've finished all of the training missions) are only for the current chapter.  Not sure why the mission you did seemed familiar though.  *shrug*  To access all of the critical missions in each chapter you need to have a reputation rating of at least 50 points for your org.

The archives are there to not only let you catch up on the story, but their completion tokens can be traded in for some cool clothing and visual effects.

another thing that you should know about missions is the difficulity level.

 easy: enemy spawns are one level below you

medium: enemy spawns are at your level

hard: enemy spawns are one level above you

I personally run my missions on hard as you get more experience and better loot from the npc's in the missions.  I belive archive missions are automatically set to the HARD level for difficulity, while regular and critical missions give you the option.

good luck

Note: the "Agents" in the chapter 1 archives aren't real agents, but impostors - note the off-black suits, glowing red eyes, wrong weapons, and the fact that they're easily (in comparison to the real ones) killed.