What is the name for "academic fights"? There are several kinds of academic fights:


Two researchers may have different interpretations or modelling approaches to the same dataset. They claim that the other party is wrong in their publications.
Two researchers claim that they did the same thing first, not citing the other's work
Two researchers claim that the other party's research method, data collection process, and coding methods are problematic. 


What are the names of these fights? How do I find recent examples of these fight?
To my eyes, your examples fall into two very different categories. 

When researchers are in conflict about who did something first, that is typically known as a priority dispute. When the stakes are high, these can be extremely bitter: see, for example, the fight over the discovery of Haumea or the fight over CRISPR patents.  The problem here is that it's not really a scientific dispute at all, but rather a historical or societal dispute, and scientific methods cannot generally help to resolve it.

On the other hand, when scientists are contending over a technical question, ultimately the fight will be settled by nature and not the scientists (even extreme political pressure can only defy reality for a limited time). When considering low-intensity conflicts, this is so common that I'm not even sure that it has a particular name---it's just a natural side-effect of the scientific method. Get any two scientists in a room together and you will find that there are things that they disagree about and are would be happy to see settled one way or another by additional evidence.  When they are larger and more persistent, they typically end up being called something along the lines of a debate (e.g., "the nature vs. nurture debate") or a controversy (e.g., "the Hopi time controversy").  In this case, ultimately there is usually some truth to both sides, and the ultimate resolution is often actually a reframing of the problem.