To come back on DocWagon: they are cool! We're still planning on playing a DocWagon HTR team, although they might be a little more violent then needed.
How to use DocWagon rule wise: Shadowrun Companion (p90-91). There are response and cost tables available. So to answer some questions:
Q. When is DocWagon summoned?
A. When you signal them (that is, if you still can). We also rule that with the appropriate equipment, you can make the call via DNI (so a mental command is enough: Cogito, ergo sum

). Otherwise: when physical track is full. Note however that they will not come when you're on extraterritorial corporate or government property (unless they have permission from the controlling authority).
Q. ...Then the person will be dead within the minute, not nearly enough time for DocWagon to get there...
A. Response after Companion: 3D6 combat turns +/- modif. (see p.91: according to where you are, are they using a ground or air vehicle,...) Now if your overflow boxes are less then your Body, you get +1 box per Body combat turns. So you can wait for maximum Body*(Body-initial overflow) combat turns. So you have a fair chance. Realistic? Nope, but eughm... they are cool?

Q. Does DocWagon use the RFID info? Do they turn runners over to the Star?
A. DocWagon doesn't want to lose there prime customers I suppose, but evil GMs always come up with nasty ideas.
Q. HTR and other costs?
A. Companion p.91 (HTR=5.000

and my personal favorite "Employee Death Benefits: 20.000

" > DocWagon Sprawl Hunt for rich people

)