If a player loses connection, and they are in a fight, will the other players around be notified?
No
But members of the group (if in a group) would be.
will an icon appear letting all know that this player is off line?
That would be the best way, again for groups.
If a mech runs back to the base when the player is off line, what happens when the mech reaches its destination?
Right now, despawn as it is considered entering into the Mech Bay. Later on, walk into the Mech Bay and then despawn.
How do you define a rule cheat though?
Discussion and feedback I think are the best way. For example, if five players ambush a solo player, is that considered an acceptable tactic or is that considered ganking and unacceptable?
if a player is in town and their computer is on a crappy wifi connection, and say they drop 10 times within an hour, will actions be taken against this player?
Not that I can see. Depends if there was a behavioral pattern with some clear objective that can be perceived.
Example 1: Login, walk 20 meters, attack NPC, Loot, spin 180, walk 20 meters, spin 180, logoff (camping spawn)
Example 2: Login, place on ground Item A, pick up Item A, put Item A into Trade-Window, Log-off (duping)