Can a $4000 per semester cash payment for school tuition and $1200 monthly credit card bills trigger an IRS audit?

No.

You didn't say in what context these payments were made - do you mean you write $4,000 checks per semester? Is it your credit card? There is no particular reason this would trigger an audit- $4,000 tuition is not at all unusual but whether or not it's deductible is another question - if you are trying to deduct it, well that might trigger some interest. As far as the credit card bill, that, in and of itself, is not really any of their business (at IRS) unless you are deducting this as a business expense or something similar.