I means "to check", "to control", etc.. Take a look here: http://tureng.com/en/turkish-english/kontrol%20etmek
I am not a Turkish expert but probably not? "Etmek" and "yapmak" both mean "to do" but they don't seem to be interchangeable in phrases like "kontrol etmek" and "dans etmek". My impression is yapmak is used more generally (e.g. I did it = yaptım) while etmek tends to be used in specific verbs or phrases such as the above examples.
It probably would never be used alone but as part of a conversation. For example you might say "Do you have the tickets" the reply might be "Just a minute, I am checking" I believe they sometimes use sentence that never would normally be used so you get good at interpreting the Turkish to English. I actually wrote "I am checking" and it was marked as wrong.