I am starting cocos2d and going through some online tutorials. The first question is arising in my mind is that is it necessary to use tiled map if yes then Why?
Can I not add a background image in scene to feel like a arena?
I want to make a arena which will have a long path in a field and player will run only on the path (similar to car race), and after a certain distance this will repeat. How will I make such environment in game. Idea, concept or reference links will be appreciated.
It is never really necessary to use a tiled map. For anything. However, it is helpful for many scenarios. So, in your case, no, it is not necessary. There are many other ways you can implement a repeating background or whatever.
Yes, of course you can.