Say i want to make a game that will consist of 1 v 1 browser or install based.
Could i do it with free unity?
Yes of course. Many multiplayer games made with unity were created using the free version
Yes, Unity Personal Edition has full support and tools for developing multiplayer games in a variety of configurations.
Speaking of configurations, can you elaborate one what kind of set-up you are thinking about for your multiplayer game? Is this 1 v 1 going to be local on two different machines, or will it be on-line. Is it going to be turn-based, or action-oriented. Will it require a dedicated server? These are all questions you will want to ask yourself as you define your requirements.