Assuming that this is a basic two channel set, with no fancy mixing, it sounds like either the TX or RX is broken, Operating the rudder should have no effect on the throttle, and vice-versa.
My best guess is a fault in the transmitter, probably in the wiring to the sticks potentiometers, since that is where the encoding is derived.
For the rudder turning too far, this should never happen unless the mechanical linkage is badly set up. The effective lengths of the servo arm and the rudder arm should be equal to prevent the rudder going over center and latching. On the other hand, if there is mutual interference between the two channels, the throttle channel might be upsetting the rudder channel.
It sounds like you set it up to act like a tiller - I think most of us prefer to use the "left for left, right for right" convention as it saves a lot of thinking.