No the check engine light will not come on
No, it will not.
The computers system registered an error during a diagnostic or a failure in one of the sensors. Take it a local autoparts store to have the code read and then look it up online.
what causes the engine light and the tcs and slip light to come on
No, the Check Engine light will only come on when you have an emissions related problem.
Open the trunk and pull the carpeting back from the rear lights and there are 3 or 4 twist nuts that you take off and the light will come out, do this on both sides.
Yes.
When a check engine light comes on the driver needs to fix the problem for the cause of the light to come on. If the light stays on, then need to perform The Stomp Test.
at about 6000 rpms
If it is easy, your gas cap is not on correctly.
It might be that you did not tighten the gas cap enough.
There are pages of causes, you need to have it checked for codes.