I want to know the difference between "Don't fight me." and "Don't fight with me.".
The sentence "Don't fight me" suggests a physical fight and the sentence Don't fight with me suggests a non-physical fight such as an argument, I would usually say Don't argue with me to make it more explicit although Don't fight with me is also a valid phrase.
The two sentences may have the same meaning if with is understood as against or opposed meanings if with is understood as alongside.
Consequently, whether they have the same meaning or not it's entirely dependent on a larger context.