At a quick glance, that charge controller looks to be one of the piece of crap Chinese controllers that are sold under various different names. This is not to say it won't work - it might work just fine. You can do what you want, but I personally would not buy a cheap "who knows what's really going on in there" controller.
Looking at the description on the Amazon page you linked, I see a few red flags...
First, it says it does an equalization charge to 14.8v. AGM batteries are NOT supposed to be EQ'd. It can be done, but most manufacturers specify a procedure of very precise voltage/amperage/time that basically requires a lab spec power supply instead of a battery charger. So if you can't disable the EQ function on that charger, don't use it for an AGM.
Then it says this: "4 Stages: equalization, PWM, Boost and Float". That's marketroid BS.
EQ is not really a stage...it's a maintenance function that's supposed to be done occasionally - like once a month for flooded batteries and never for AGMs unless there is a specific problem with the battery.
PWM is not a stage at all, it's a type of charge pulsing.
Boost and Float - some manufacturers use the word "boost" instead of the word "bulk". Bulk is an actual charge stage - basically feed the battery all it wants until it reaches 14.4v. Float is when the battery is charged and the charger drops the voltage to just keep the battery topped off. A 2-stage charger does a bulk stage and then drops to float.
So translating the marketroid speak into plain speak, it looks like a "2-stage PWM charger with some sort of EQ function".
If that really is what it is, it will probably do a decent job of battery charging. And if you can disable the EQ function, it probably won't toast your AGM.
As for your questions about charging the battery from the truck's system. ..
Answer to A) is: No danger of over-charging. The battery will get charged to the same voltage as the rest of the "12v bus" on the truck. I.e., the same voltage as the battery under the hood.
Answer to B) is: No ill effects to the truck at all.
The only real gotcha is drawing power from the aux battery and backfeeding it into the truck. It won't hurt anything, but replacing the blown lighter fuse every time the starter tries to suck all available power might get annoying after a while.
There are several different manufacturers of the lighter doohickey. I would assume that they have a diode to prevent the backfeed problem I just described, but I haven't done any real research into those devices.
Current: 76 E-250, bubble-top, self-contained|couple of old Yamaha enduros
Previous wheelers: 41 Willys|78 FJ40|78 Bronco|84 Bronco|74 Ramcharger|78 Ramcharger|79 D150 PowerWagon|77 D100|79 D400 dually, converted to 4WD, utility bed, 10' Lance|75 Westy|69 Scout, RHD|bunch of others|bunch of bikes|couple of boats|couple of motorhomes|blah blah|so what|not my idea|just doin' what I'm told|wank wank|this space for rent|candy is dandy|but liquor is quicker