I had a right-sided tumor, which did not present symptoms until I had a blockage and had progressed to Stage IV. No bloody stools or anything like that. When diagnosed, I was 8 years out from a clean colonoscopy. I did have frequent lose stools and diarrhea, but that was almost certainly because of metformin. (I'm still on metformin and it is still an issue for me. Having 30% less colon obviously doesn't help!
My tumor most likely sprang from a sessile polyp in the hepatic flexure. Such tumors are difficult to detect at an early stage. As to your question about whether one can have benign polyps on one side and cancer on the other, all I can say is that my recent colonoscopy revealed two benign sessile polyps on the left side. So yes, one can.
Personally, I don't see any point in a sigmoidoscopy. It may eliminate the possibility of rectal cancer, but it fails to examine most of the colon. It certainly wouldn't have found my cancer.
ETA: The issue of comparative prognosis for right and left side tumors is complex. A few years ago, they would say that right side tumors had a worse prognosis. This was because of several factors. First, perhaps, that as stated here they tend to show fewer symptoms early on, thus they are often discovered at a later stage. But another thing is that right sided tumors are more likely to be MSI. KRAS mutation is also somewhat more likely on the right side. MSI tumors respond less well to FOLFOX, and MSI/KRAS tumors even less so. Since the advent of immunotherapy, this is turned on its head. It is important to put all prognosis generalizations in context.