Ninja cat is a summon. You get summons at level 50-53.
A good starting F2P team is
Fire Main, Hinata, Kakashi, Kankuro setup like this https://i.imgur.com/umcIXTh.png
Set up your talents like this https://i.imgur.com/K7u6anq.png
This is great damage and good combo. Here is one Combo
1 - Main Mystery - Fire Style Dragon Flame Jutsu
2 - Kakashi Fire Ball Jutsu
3 - Main - Celestial Prison
4 - Hinata Sealed Point Palm Strike
5 - Hinata Gentle Step Twin Lion Fist
6 - Kankuro Black Ant
7 - Kakashi Lightning Blade
Great damage, plus you get Acupunture on there from Hinata (They can't use Mystery Skills), they are Ignited from Kakashi (take damage at start of round and prevent healing) and they are Paralyzed from Kakashi (Cannot use Chase Skills)
You can replace Kankuro with Kabuto, too. You will do much less damage but you will have the heals.
Hope this helps!