Patxipt,

When you say that “he mentioned I shouldn't aileron bank in turns past a certain amount”, I understand that you should input aileron only for enough time to bank the wings and then return the stick to the neutral point.

Once the wings are banked, the model will start turning because part of the lift force produced by the wings will point to the center of the horizontal circle that the model will follow.
The bigger the bank of the wings, the smaller that circle described by the turn will be.

The problem is that the lift force produced by the wings is now divided between the vertical component that keeps the model floating and the force that is mentioned above.
For that reason, the model that starts a turn will start descending at the same time.
In order to avoid that, and to keep the turn at the same level, elevator up needs to be input.

If the natural loss of altitude created by the bank of the wing is not compensated by the elevator, and the aileron input is kept for too long (“past a certain amount”), the model will roll and descend continuously, steeper, tighter and faster into a spiral dive.
With sufficient altitude, the model can be saved, stopping the roll and fall with the proper controls.

The slip that your instructor mentioned is a sideways movement of the model relative to the airflow (it does not follow the circle of the turn), in which the nose of the model points towards the centre of the turn.

A proper level turn requires the use of ailerons, elevator and rudder, each in the proper amount.
Such turn is known as coordinated turn, which is better explained in this link:

http://en.wikipedia.org/wiki/Coordinated_flight

Regards