Relaxers...

Well, the point of a relaxer is to 'unpoof' hair - that is, break the chemical bonds that hold hair in whatever natural state it may be in. It is permanent. BUT! Any new hair that grows will be in the natural state, meaning you'll need a touchup about six weeks. Since you're essentially pouring chemicals into your hair, yes, it is bad in that it makes your hair weaker than it ought to be.

As for whether or not an in-store relaxer will be strong enough to straighten your hair, I would look for a box that has a model that looks like you to start with, and from there look for a weaker or stronger formula based on just how kinky or wavy your hair is.

Correct. But ONLY the new growth! If you overlap and put chemicals on previously treated hair, you're asking for breakage and weak spots.

The current wisdom with relaxers and color treatments seems to be to wait about two weeks before adding color to relaxed hair. Your hair needs about that long to recover adequately. You can wait longer, but don't do it any sooner, or once again, you'll be asking for problems.