The ability to fuse DAS and radar tracks and construct a common 3D picture of the air battle, with integrity and reliability sufficient to launch missiles, would be truly impressive but has not been demonstrated. Given that DAS alone is inherently 2D, it would be quite challenging.
Yes, one can launch AMRAAM within visual range. If you were strong enough you could pick it up and hit your adversary over the head with it, for that matter. What it won't do very well is high-off-boresight at close range because it can't pull the g off the rail.
As for jamming: The limits are as JTO describes, as far as I am aware, although there is a towed or expendable system (BAE ALE-70) for use when the aircraft is carrying external stores.