Yep. The katar is an Indian weapon *sadly I don't know much about it coz I kinda dislike it*
No, its not related to the katana in way other than being a knifing tool!
A katar is a more fluid weapon to weild. First up, it's got a small blade so its used for close combat only. You can directly see that your defence perimeter is going to be very limited with such a weapon. On the other hand, its easily manouverable so it allows for a more fluid fighting style.
You could think of it as the "sai"... the weapon that...lemme see... raphael uses in TMNT. It's also the one Elektra weilds. They are small weapons too and they rarely have a sharp edge. Fighting with Sais usually involved piercing with the edge and blocking with the blade.
I guess I confused you now more than clearing up things...
...sorry it's a blood trait of mine *Mwahahahaha*