To answer the rest of your question:
AKBAN, which is what I take. http://www.akban.org
It has all you listed, except acrobatics, and more. Even firearms training:
If you want to learn flips and all that go and do gymnastics. If you want to learn how to use swords take up fencing. If you want to take up a martial arts then there is a variety of options like mma, muay thai, boxing, sambo and so on and so on.
Probably the best thing for you is xtreme martial arts. Despite the name they have actually very little to do with martial arts. It's more about looking cool, jumping, flipping and all that. Probably the last thing I would use for self defense but I'm sure it's a great deal of fun. Another thing for you might be parkour, which is also quite cool. And no you can not learn most of this online or through watching videos. You need an instructor or at least some group of people who know more than you do.
well, there are different types of Martial Arts. I'll suggest you the following
Wing Chun for punches
Taekwondo for kicks and acrobatics (also contains flips)
Jodo for Throws
Kung Fu for swords
you can learn all online and by watching movies this is called mixed martial arts
What has acrobatics and flips got to do with Martial Arts?
I don't think you wanna train, I think you want to dance. Go join a dance class.
Martial.arts is just a seminar money making con business..try boxing...
wushu
eagle claw
xma
tkd
chou lay fut
monkey fist
I think your looking for capoeiro
Is there a martial art that includes acrobatics, punches, kicks, throws and how to use a sword.
It doesn't have to include all of them but try to include most of them.
no mma please.