I need help Building A Solid state Electro magnetic Mixer
Firstly, may I suggest building the simple version (using a magnet and motor) first, then building this idea when you're more confident with electronics?  This is some advice I have found useful in my experience--start small, then work to make it larger.

Now, do address your questions:


As far as I can see, it should be feasible.  The concept is similar (in some ways) to the way a stepper motor works.
Please define "simple components," and from what perspective they are simple.  An Arduino would be a very simple way to control the magnets (from a programming perspective), but it isn't a simple component electronically.
The usage of your 10 kOhm pot is feasible, but exactly how depends on the answer to (2).
Again, dependent on (2).
It depends on the length of time you're running this...  I doubt it, though.


You'll be able to get better answers when you have more specific questions...