How do trucks get onto the tracks at GCT?

The other day, I saw a railroad service truck (with the miniature flanged wheels in front and back so it can go on either paved roads or rails) sitting on Park Avenue. This got me thinking about how it got there. Is there some street entrance to GCT where a road vehicle can find its way onto the tracks?

The hyrailer probably would've gotten onto the rails at MO and traveled to Park Avenue and GCT

Correct, either a conductor flag or someone from MofW will pilot track cars to and from Mott Haven into GCT. The conductor flag will handle outside contractors and MofW personnel will handle MNR hi-rail vehicles.

and how do those trucks get back out of GCT to MO to get back on asphalt?
are they double ended ?
or must they use the loop (upper only these days)

its all a gear shift thing, put little handle in R and use mirrors.

Every day there are trucks going in reverse between Croton Harmon and Tarrytown with the ongoing Sandy work.

Worth noting that going in reverse is much less of a big deal when you're on rails and don't need to worry about steering or oncoming traffic.

How fast can these trucks go? I assume the tiny little wheels are not as stable going over switches, junctions, etc as the full-sized train wheels?

Truck type hy-rail is allowed 30 mph(forward) 25 mph (backward) on straight rail, 5 mph over switches, and must stop when a train is passing them.