The concept of self defense assumes you are using as much force as the attacker,
not more. If someone punches you, you cannot shoot them and claim self defense. You are allowed to punch them back though, and the courts do see this as self defense.
On to martial arts and professional athletes now.
In both cases, a champion in those forms is always considered armed. So if someone punches
Zambidis and he punches them back, Zambidis is the one at fault for using excessive force. If the attacker has a gun though, Zambidis' punches may be considered an appropriate force to respond with.
On the carrying weapons on you part. Martial artists are allowed to carry their weapons with them, though under conditions. If I walk around with a sharpened katana on my back, the police have every right to detain me. If a martial arts teacher with katana specialty walks with the same katana on his back, and he does have the proper paperwork with him, he is allowed to continue on his way, even though he may have to go for verification before been allowed to.
Using said weapons in a fight though will most likely result in an excessive force charge, since not only is the wielder already considered armed (martial artist), but he is also using a weapon. Not sure what you'd have to attack him with for the katana to be considered appropriate force.
And finally, you do not learn a martial art to beat the crap out of others. You learn one to prevent someone from beating you up. If you can't see the difference between the two, then I doubt any teacher will be proud in whatever you learn.