How many chest and abdomen CT scans before I start worrying about radiation causing cancer?

Radiation exposure. From ct's has been under-appreciated, now over-blown in importance. It is a major issues for populations, and trivial for an individual. You should never get an x-ray of any kind that you do not need. X-rays are carcinogens, but very poor ones. A ct scan has 10-100 times exposure of a chest x-ray. Get the imaging that you need; don't over do it. Don't worry. (mr & u/s = 0 x-ray exp).
There is no number. There really is no set number. There is a low dose of radiation in imaging studies and over many years repeated exposures are not recommended. The risks have to be balanced with the benefits and there may be very good reasons that you need to get imaging studies done. The technology used today is much safer than its ever been and there are low dose scans available for certain situations.
Many. Its never a good idea to be exposed to radiation for no good reason, but the radiological society of north america estimates that a ct chest is equal to about 2 years of radiation exposure we all receive in normal life, and abd ct about 5 years. They feel this adds a "low" risk of cancer. Newer techniques appear to cut the dose/risk to 25 % of this. Ct is a major diagnostic aid today.