There are pages and pages of things that can cause a check engine light. You need to have it checked with a scantool. Then the code can be diagnosed and repaired.
It really depends on what the cause of the check engine light is.
Yes you can. But you will want to check you're engine soon.
It is safe to drive you car for at least one mile after the check engine light comes on.
yes
It is not recommended. A flashing flashing check engine light is an indicator of a catalytic converter damaging misfire.
Definitely not, get it checked imediatly
yes
Yes but, if the light is flashing no.
If you fix the reason the light came on in the first place the check engine light will reset itself after a few drive cycles.
You have to get the engine looked at.
Replacing the battery should not have triggered the check engine light. The check engine light comes on when there is a problem with the emission system. Saying that, I would drive it for a while to see if the light does go out. If the light does not go out have the ECU scanned to retrieve the trouble code. Then use this code to diagnose the problem.
You must be kidding. The check oil light means, Check the oil level. It is either low or the oil pressure is low. Check engine light means the computer has detected a problem effecting the emissions output of the engine. Call a professional. Do not drive this car.