When your check engine light comes on a code is stored in the vehicles computer system. This code is vital in troubleshooting the vehicle accurately. To access this code requires a scanner that most any auto repair shop or auto parts store such as Advance or Autozone will have. Most establishments will scan the code for FREE. My recommendation is to have the vehicle scanned and send the code to me. I will take it from there and will be able to better assist you.
Let me know when you get it, take your time.
I didn't mention anything about a mechanic....those are auto parts stores that will scan the codes for free in about 5-10 minutes. Trying to speculate without knowing the stored trouble codes would be an irresponsible guess. I prefer to give you more than that.
I would compare it to trying diagnose the human body...without an x-ray or an M.R.I.
As for tire pressure, no. The gas cap can in fact make the check engine light come on, but will not activate the VSA light also.
The check engine light can come on for over 50 different reasons.