Two part question...

1) What exactly are the advantages of being jumped into a device within mutual signal range over a longer distance matrix connection?

2) If a rigger is jumped into a device, is it possible for a hacker to also jump into said device and try to kick the rigger out?

Second question first, yes a hacker can just boot you if he hacks the system and kicks you out. The fiction in SR4a at the start of the unwired world section talks about exactly this happening. Once hacked a drone's node is the same as any other node. This is why the drone rules are in the unwired section rather than the vehicle rules section at the end of the combat section.
Ok first question now.
There aren't any really beyond being able to react to the situation faster. If you are on site with a drone and someone jams you, you have a better chance of dealing with it. You can take out the jammer or enable your own counter measures. At a longer range you just lose contact with your drone and need to find another way to it. Either situation has advantages and disadvantages tactically.
With the long distance option you are protected from direct attack and may be harder to track. You sort of gain plausible deniability if your drone gets tagged. But you lose a hands on on feel for the situation. Its best for surveillance jobs and the like.
With the on site option (mutual signal range), which can be quite long range in itself, you have a direct connection and don't need to worry about the linking systems dropping off line, can react to things like jamming more immediately and actually see what just dumped you offline (assuming dump shock doesn't disable you). It is best for attack drones and the like.
I'm sure others have their own ideas about how to use these but this is how we generally work it. I can't wait to see how I'm wrong

i'm just going to add that you can't spoof a drone that has a rigger jumped in. it stops taking all other commands, even ones from it's own pilot.

1. No mechanical advantage. Either situation has implications.

2. "A jumped-in rigger overrides any other control of the drone, including by its Pilot." p. 246 SR4A Now whether this extends to a Hacker doing Exploit and then sending a shutdown command is an interesting question.

Since a jumped-in rigger needs an active subscription in the drone's node his icon is present there. After a hacker has gained access to the drone's node he could do all kind of evil things with the rigger's icon... And of course he could try to crash the drone's node, but since the rigger is also there and will have admin rights too, he will most likely become aware of this.

-CJ

The Netcat vs. Slamm-O! scenario neatly describes how a jumped in rigger can be kicked out of a drone. CeeJay is right, the rigger's icon is in there and can be engaged in cybercombat. However, CeeJay's post implies that the rigger's icon is just sitting in there helpless, but that is not the case, he can still do everything a hacker can normally do inside the node, including initiating cybercombat with intruders.

Obviously, any actions he takes against icons in VR are actions not being used to control the drone so even unsuccessful attempts to boot the rigger can provide a nice distraction.