Not sure about the screws and plates being weak spots. I don't know why they would be, but that's beyond my knowledge base.
Yes, often bones do heal to be essentially stronger than they were prior to a break. I believe that thought process applies to bones that were broken "normally," not from surgical cuts (I don't know if that would matter or not, but I don't see why it would). Also, I think it's important to remember, if your mandible is cut and moved for jaw surgery (for example) the osteotomy sites may heal to be marginally stronger than they were prior, but your whole mandible will NOT be stronger. This is also only applicable to the normal, healthy person (tons of stuff can f**k with bone remodeling).
Yep, if a person fractures a bone, there is often additional calcium deposited at the break (sometimes visible, if only temporarily, on an X-ray, MRI or CT).