How to understand free jazz?
Some genres and styles (not exclusive to jazz) are based on very well stablished and known patterns and dynamics: specific cadences, progressions, scales, rhythms, instruments, etc.
Free jazz is a very loose concept that tries to label improvised performances that try to cut away those common conventions. As you walk into the realm of the uncommon, things start to sound strange.
Do you need to know music theory in order to fully appreciate Free Jazz?
It depends on what you mean by "fully appreciate". If you want to analyze a performance and study what is happening, why, and how, then music theory will be helpful. But if you want to just listen and enjoy, then music theory is unimportant.
I've played free jazz tracks to friends with zero music theory knowledge, and some of them have loved it to the point of starting a free jazz music collection. Other friends, including people that make a living out of music, have given me the "what is going on, I don't want to listen to this" look.
What is it that makes free jazz harder to understand than, say Bebop?
Many genres and styles are based on patterns that are familiar to the listeners. Bebop in particular has a bit blues, swing, gospel, ragtime, and theory that can be tracked all the way to the common practice period (baroque, classical, and romantic).
Free jazz tends to say goodbye to many of those patterns, so you can find it harder to understand. The idea is to free yourself from those conventions (both as a musician and listener), and explore what is beyond those limits.
It can get chaotic (not necessarily), as musicians can all be playing different harmony, rhythm, and perhaps no other framework than "no framework". They might even deliberately try to stay away from each other's structure. In other words, it can get really really weird.
Besides Coltrane, Ornette Coleman, and Sun Ra, which other musicians who do Free Jazz would you recommend me?
@user135395 From the top of my head: John Medeski, Kris Davis, Matt Mitchell. Any good internet radio station should have free jazz related channels where you can surf endless free jazz performances and buy whatever you want. I use Accujazz.
Try Tomasz Stańko, especially "Freelectronic/Pejotl" for some mixture of free trumpet with free analogue devices coupled in different configurations by Andrzej Sudnik. The second album is composed to early XX century peyote tripraport by Polish painter/playwright.
Oh, and maybe also "Miłość" with Lester Bowie. It's free jazz, but it is well, a bit easier for newcommers.