You can't decide to buy hits in a situation, and I don't expect the GM to allow it in situations where actual risks exist. Probably best if the GM simply rolls for the Agent's perception when it matters, and you just roll twice. (I actually had someone roll multiple Clearsight checks to aid another drone in Clearsight.)
By the way, you don't get to raise your Limit with the hits of a helper on a Teamwork test. If he scores 1+ hits, you get the hits as bonus dice and a +1 to your Limit.
Matrix isn't my strongest point, but you will automatically spot icons (and probably filter them by type, so not looking at any non-guns/commlinks) when in AR/VR. Of course the GM decides whether they run silent.
Agents are autonomous programs, I assume they have their own Initiative since they can run without supervision on their own devices. My guess is that their Initiative is like Pilot programs, since they're similar to them, so Ratingx2+4d6, but I wouldn't really know for sure. However, Pilots, IC and Sprites all have that as Matrix Initiative, so I'd assume Agents are no different.
Your Agent can't score marks for you to use, because each Persona has its own Marks and they cannot be shared in any way. Note, however, that it MIGHT be possible for Spoof Command to spoof the Invite Mark (which requires Owner) command, though I don't dare make a statement on that matter.
Teamwork tests may very well be possible, though I probably wouldn't allow them on things that have an effect on you alone (so scoring marks). However, perhaps this should in fact be possible, so I can't really tell. It WOULD solve the matter that right now even scoring Marks on multiple opponents is incredibly risky because failing once = bloody hell. As such, it might actually be fair, since it requires high expenses and a program slot to be sacrificed. Definitely something we can use official clarification for.
DURING Combat Encounters you're a bit limited, might be best to just do Attack Actions then to brick gear, or score a Mark and then start ejecting clips. What you want to do, however, is find out there's enemies BEFORE combat starts, analyze their devices with Matrix Perception, score Marks and run Trace Icon. That way you can make AROs for the entire group to use so they know exactly where some of the enemies are. And when combat starts you can immediately start ejecting clips or shutting down cybereyes, or brick weapons.
Just keep in mind that the second you start doing this, people will know they're being hacked and will turn off their wireless. That is of course a bad thing for them as well, but it's also why attacking for bricking isn't a good idea: They are immediately aware so unless you brick them (and your Agent can help there) before they get their turn, it's useless.
By the way, you're correct in that Ejected Clips can easily have a fresh one reloaded (barring the few idiots without spare clips). However, you're forcing someone to sacrifice a Simple Action to reload, meaning they can't use one to dive for Cover and fire at the same time, or use Suppressive Fire. It also costs them their Free Action to turn off the wireless. So basically you're costing them a Free and a Simple action with a Free of your own. One downside is that following the Missions FAQ, this probably counts as an Attack action so you wouldn't be allowed to eject 3 different clips. (We'd have to ask Bull for that.)
Bricked Weapons, while not capable of firing, can easily be fixed with lengthy Hardware checks. So it's not as if Bricking the gear destroys it, as long as you're willing to fix it afterwards before fencing.