Would it be weird if I passed up a CT scan and requested a sonogram instead to check for kidney stones?

Not necessarily... Ct is the most sensitive test to look for kidney stones. Very small stones or stones outside the kidney (i.e., in the ureters or pelvis) can be missed by ultrasound. If worried about radiation, there is a low dose protocol for ct that can be used to look for stones. The amount of radiation exposure for low dose ct is about the same as a plain x-ray. Ask the imaging center if they perform this.
No. Ultrasound is a very good test for kidney stones provided they are able to get good images (and less radiation). Limitations of ultrasound would be obesity.
Not necessarily. Kidney stones can be seen on ultrasound and plain xrays at times.
No. A kidney ultrasound will see kidney stones but will miss stones already in the kidney tube (ureter). There is also no radiation with ultrasound as compared to ct scans which are much better for detecting kidney stones but have a lot of radiation associated with the test.
No. But having said that a ct scan is better than ultrasound for showing kidney stones and their complications.