It would only affect bowel movements if the tumour had either become so large that it blocks the bowel, or has spread to the bowel or has spread to the spine and caused spinal cord compression.
A would be detectable easily by a GP or urologist. B would be more likely to lead to blood in the stools than constipation. C would have other symptoms like lower limb paralysis or numbness. All would usually be evidenced by a high PSA reading.
The nost common cause of constipation is dehydration. A common cause of loose stools and urgency is IBS and foid intolerance although there are many other causes.
Best to see a GP to discuss.
"Life can only be understood backwards; but it must be lived forwards." Soren Kierkegaard