Infiltration is a major topic of the challenge video, but it's definitely a good thing to talk about. When you infiltrate it can take either very little time (Tier 3 Infiltration, generally an innkeeper) or a long time (Tier 1 - Corrupting the Minister of Defense, a High Priest, etc) with the options in the middle being the most Common (Tier 2, Corrupt the Town Watch, Guildmaster, A Lesser Noble). These infiltrations are almost ALWAYS permanent as long as you don't "use them for favors" OR the heroes/nations are ACTIVELY hunting your influence down (late game).
We came to this design after many, many tests - we originally had it as a "currency" that you kept up by doing Infiltration actions, and then you "expended" the currency to do certain actions or events, then we had it as a "Rumors" system where you could get more/less information based on the importance of the action and how far it was. This system offers the best combination of risk/reward, and prevents it from being tedious.
The other element added was the "using them for favors" as I mentioned above - this came relatively late but really solidified the approach. Basically whoever you have chosen to infiltrate can perform a favor, but if you use this favor it generates a quest (possibly very low threat so no one will come, but it is additive). For example, the guards can arrest a pesky adventurer, a Noble can temporarily lower the Security for Tier 1 actions, or an Innkeeper may cover up a clue for you. It's a great blend of theme and functionality while also forcing you to leverage your most fundamental plans (infiltration).
As far as actions, each Agent can do any number of things and then perform a challenge. That's not to say they will often have a lot of things to do outside of challenges - almost anything you gain adds an "action" to the challenges, this includes skills, artifacts, and imbued powers. You may use any number of Old One powers (also sometimes referred to as Ancient Powers) in a turn as long as you can pay the cost. You may also activate any number of agents as long as you have a free slot and enough Ancient Power to pay the cost. On turn 1 you will almost always summon in the three "early" heroes, which brings you immediately up to 4 challenges being performed.
All that being said, getting blindsided IS a major element of the game - we tried to invert the standard idea of heroic gameplay and lay you in the role of a stereotypical villain. Random interlopers is part of the joy (frustration) of the game, but here is how we "tempered" it. When a Hero shows up in a POI you are performing a challenge in, he doesn't immediately attack you - if the threat is sufficient he begins to "hunt down the source" of the disturbance. His skill is increased by your Profile - if you are a famous hero from publicly murdering several kings and burning cities walking around with some frost giants he will find you almost instantly - as you might expect. If you are a crafty corrupted nobleman who has maintained a low profile by performing only low tier tasks or obscuring your higher tier ones it would take them some time to find you, allowing you to finish up with your fiendish challenge and then escape.
What does this accomplish in gameplay terms? You will have an idea of when an Agent is going to be pursued, found, or otherwise forced into uncomfortable situations. Perhaps you'll only use this agent tactically, in areas you have either reinforced or have infiltration around, or maybe you'll embrace his reputation and send him with powerful minions to a trap-filled ruin, hoping to lure in and kill his pursuers (increasing his danger even further). It also adds a "time bomb" effect to Agents, forcing you into these difficult decisions instead of being able to coast with a consistent strategy.
If you get interrupted and defeat the heroes, you can continue as if nothing happened. Of course, they may rally and return but hopefully you'll be done by then. You can always opt to Flee (after 1 round of combat, and losing all your minions) or retreat (after 2 rounds, and escaping with your minions). You have two major means of casting "spells" in combat, one is Old One spells which are generally rare - we didn't want global instants being a component of the game - the other is teaching your agent spells, which once equipped can be cast during combat. Some of them are suitably devastating, though most have some kind of drawback.
EDIT: We may be making all "Champions" (powerful heroes at game start) visible on the map at all times, it currently only shows them if you have mid-tier infiltration in the capital of their country. These are your "big threats" early-mid, because they can stomp on your early agents.