Finger check will usually only detect a huge prostate or rectal cancer(not other portions of the colon), or a rectal cancer just next to the anal canal.

Colonoscopy(can detect polyps BEFORE they become cancer, but more costly and hard for patient) is the gold standard for detecting colon cancer, along with fecal occult blood which is cheap and easier to do but will detect only more advanced cancers. For prostate, the early detection and screening is usually using done using a PSA blood test.

Not a doctor, but my SO is one. AFAIK the finger is used to check for prostate inflammation/abnormalities. Colon cancer checks are done either via analysis of hidden blood in feces or colonoscopy.

At best, I can imagine this being a rectum cancer check, not a colon cancer check - the colon is around 1.6-1.7m long. Even the rectum is longer than a typical finger (typically ~12cm long according to Wikipedia).

You cannot reliably assess for prostate cancer using an ultrasound. PSA blood test in concert with rectal examination of prostate, with MRI of prostate of abnormality detected as the next step.