This is a regional terminology problem for me - what do you mean by "ground beam"? Where I am, we have grade beams and continuous footings. Grade beams span between pile caps in deep foundations (driven piles, drilled piers, etc.) and a continuous footing is a shallow foundation relying on the bearing capacity of the soil. I believe I've seen ground beam used to describe both of these before on this forum.
Since you're concerned about length, I'm going to guess that you are referring to what I call a grade beam (please correct me if I'm mistaken). So...
1) Length is limited the same way the length of any beam is limited. When using deep foundations, it's important to not rely on the capacity of the shallow soils beyond using them as a casting surface (though even that may be difficult in some situations). So your length is from pile cap to pile cap. Design for strength and deflections as you would any concrete beam, but keep in mind any additional cover requirements to protect the rebar and account for imperfections in the excavation.
2) Depends on where you are. As retired13 mentions, frost may be a consideration. I'm not sure where you are, so I don't know if it is. I'm in a moderate climate, and frost depth is barely a foot down. So I can have a 2' deep grade beam stick 6 inches out of the ground if I really want to. There are other considerations, too, like expansive clay. Give us more information on where you're located and the environment and you can get better answers.
3) That has to be worked into the overall structural design and consideration of expansion joints. Once those are located, you have to manage restraint stresses vs. anticipated movement and detail accordingly.