Can constipation cause pain anywhere in the abdomen?

Pretty much. One reason is the distribution if the nerve endings in the abdomen that does not allow for precisely locating the pain. Spasms along the gastrointestinal tract may contribute also.
Yes. You need to careful about blaming constipation for abdominal pain. However, it can cause discomfort mostly in the form of bloating or a feeling of being full, cramping anywhere but mostly in the lower abdomen, and also pain in the pelvic or rectal area if stool cannot pass.
Yes. Yes, constipation can cause pain anywhere in the abdomen.