HERE IS A DIAGRAM IN AN ATTEMPT TO CLARIFY
You can see that the blue wave (electric field) moves up and down across the centre line. If you measured the electric field at any one point it would be +ve or -ve (or zero, mebbe). But the is continually varying, and you have to think that +ve and -ve actually mean in this case, so this is where you're heads will probably explode...
That diagram actually only shows plane polarised light, you can also have the E/B field vectors actually rotate at some predefined rate (circularly/elliptical polarisation), in which case "polarity" of the wave means NOTHING. In the plane polarised case the +ve/-ve direction depend entirely on the particles that emitted them, and there may not be a clearly definition axis in this case anyway.
Really what you need to look at is that when the wave is pointing in a given direction, it will exert a force on a 'polar' molecule (i.e. one with a +/- direction bias) and when it oscillates back to the opposite direction the molecule will go in the oppposite direction - essentially the molecule vibrates with the frequency of the microwaves.
Most "light" is plane polarised.
In regards to the ionising radiation, this is simply what radiation is able to ionise a given atom. To do this it needs to knock an electron out of its shell in the atom, so for a given element there's a set amount of energy needed to do this. Low UV is just about enough to do this in some atoms, but it can't penetrate, which is why we get sunburnt.
Visible light doesn't have enough energy to do this, nor do anything below that (IR, Microwaves/Radio (there's not functional difference between a radio/microwave or really IR/micro, it's just a definition - RADar actually uses microwave frequencies)). If microwaves were enough to cause ionisation and hence cancer, we'd be fucked as visible light would be much worse.
Any other questions?