Clay barring a car must be done very cautiously, as you can mar your paint a whole lot more than even with a poor wash technique.
No, you do not need to clay bar everytime you wax.
a 10-15$ paste wax under normal driving conditions will be gone in 2 months... 3 at MOST. I highly recommend Menzerna powerlock. It is the most or one of the most durable sealants on the market right now and is very slick and helps to keep the car clean. Waxes are mainly for looks... they do help, but sealants are what do the hard work. The powerlock is a little pricey and you will have to order it, but it's worth the extra money, as a little goes a very long way.
Washing the car you want to make sure you have plenty of sudes... forget the MF wash mitt and go to lowes and get a grout sponge made by proline. The small holes in the sponge are very easy on your paint and much of the dirt will be trapped inside of the holes and therefore will not scratch the paint. If you clay the car to much you WILL get scratches and they will have to be polished out.
The key to washing and claying is making sure the surface is as slick as possible.
I don't think a clay bar will remove your wax, but it will at the very least cut into it a little.
I would either read my sticky on how to wash and detail, or go to autopia.org and read everything you can. Most OTC products are crap... plain and simple. You don't have to spend a fortune on products, but knowing which ones are best for the money is key.