Some do, many don't. Lots of meds can cause constipation. Narcotics routinely do, iron and calcium supplements can; calcium channel blockers (bp/cardiac meds) can; Parkinson's meds, antidepressants (tricyclic more than ssri), sucralfate (ulcer drug), Cholestyramine (cholesterol med), many other prescription and otc drugs. Check with md if new symptom, med change, worsening, pain, bleed. Diet, hormones can play a role.
Yes. Some medications like oral antibiotics can cause GI upset which can result in constipation or diarrhea.