Does constipation cause toxins to build up in my body?

No. Stool is not toxic. It is just left over food materials, bile and bacteria. All of these things are present in your colon regardless of how frequent you have bowel movements. Your colon is designed to have stool in it.
Rarely. For the most part i agree with dr vinson but in patients with advanced liver disease constipation is to be avoided. The mechanisms involved are complex but 'toxins' can affect these patients and can be largely avoided by avoiding constipation.