If you're passing a kidney stone you may experience diarrhea as a reflex reaction from the pain and vicinity.

That would be possible, but there are so many different causes, of both symptoms. You ought to see your doctor.

No. Everybody after age of 50 or even younger if any history of colon cancer needs to have colonoscopy. Please see a gastroenterologist

Kidney stones can cause blood in your urine but do not usually affect your bowels. You should be clinically evaluated by a doctor.

Kidney stones cause pain sometime so severe that patients are put on pain medications. Several pain medications especial opioids cause constipation. Your irregular bowel movement may be due to the pain medications you're on. The blood in your urine is most likely because of the stones. You should report both things to you doctor ASAP. Hope this helps.

In my experience, kidney stones rarely cause irregular bowel habits, although they commonly cause N/V and abdominal pain. Some types of stones, however, are caused by the same bacteria that cause diarrhea (Proteus sp.; Klebsiella sp.). If you have also blood in the stools, I would complete a workup for a bleeding disorder, or medications that can cause bleeding.

Possible but due to the excessive blood loss into your urine you need to cure your stones