The truth is, most RPGs are suitable for playing on a forum.
I've been playing D&D 5e over at Myth-weavers and rpol.net for a few months now. If you visit that site, you will find many RPGs being played, with free rules, few or no pictures etc.
However, I've only really been playing dnd 4th and 5th edition on forums. 4th edition requires lots of maps and images and isn't free at all, so I can only give advice for 5th edition. But I strongly recommend that you look at other games on those websites as well.
It can be played through text, with a bare minimum of images.
5th edition works well with theatre of the mind. Images are an option if you want them, but they aren't required. Most battles we have had at myth-weavers
No minimum or maximum number of players. We can be as many as 10 and as few as 3. We want the game to be enjoyable no matter who is available to play.
With the new DM rules out, you have what you need to play with as few as 1 character and as many as you can handle.
Players should be able to miss sessions without breaking the game. Only players present should earn advancement or improvement for their characters.
When you play by forum, there is no real "session" that you can miss. There is a running record of all actions in the forum posts, and by it's nature it's played slowly. I have seen some games were xp is rewarded based on post length and frequency.
Easy to learn. There are people in my forum who have never played and RPG before.
5th edition is made for new players, and there are many resources online to help you in any other that you might get stuck on.
Casual. I would like a fun game rather than a highly complex one.
5th edition can be as simple or complex as you want it to be. I even played one game where none of us took classes, but only used backgrounds and Racial choice. It was a lot of fun.
Free. The rulebook and the needed stuff (maps, names of characters, etc.) are free online.
The Basic rules are free and can be downloaded here