1. It does make sense because fought is the past tense of fight which the sentence is referring to.
2. No, it doesn't always have to be. It's sometimes. It can be past like the sentence in number 1 where there was a past form after "always". Or there can be a present tense to. Like the sentence: "They always fight over the last piece of cake." Here there is a present tense after "always". So the answer is sometimes.
Hope this helps.