Okinawa is the country of origin for karate. The word is made up of two characters. The second one is te, meaning hand. The first can mean two different things, though it is said the same way. Kara can mean China and was the original term used. Later, in an attempt to distance themselves from China, the Okinawa masters stated that they would use the meaning of Empty.
Karate is practiced in bare feet. The karate uniform is called a gi.
Karate means open hand, no weapons
Karate Kid's real name is Val Armorr.
Jaden Smith's name was Dre Parker in Karate Kid.
Karate-ka - Karate student Sensei means "teacher" Sempai means "Senior" (as in senior karate student)
Not unless it is at the start of a sentence or part of a formal name. Karate is studied in a dojo. He went to the dojo to study karate. He studies Shidokan Karate.
It is called karate in every country, using the name given to it in Okinawa.
Cobra Kai.
That will depend on what it is you are looking for. If there is a specific style of karate, your organization is probably the best bet. If you are looking for karate in general Mark Bishop's book Okinawan Karate is a good source. Haines Karate's History and Tradition is another source.
* Shuri ryu Karate * Shorin ryu Karate
You do one technique, and then another.
There really is no equivalent word for karate. Many will use the style of karate, such as Shidokan or Shotokan or Isshinryu, but that is a sub-set of karate rather than saying the same thing. And karate is a sub-set of martial arts, so that is not the same.