Is there any way to define the keys?

if there is not, (which I assume there is not).. then what are the keys? So far I have the arrow keys to move and turn, left click to activate and right click to swing weapon.

what else do I need to know?

You cannot define keys, but shift+M opens up the map and allows fast-travel, J is responsible for jump, U is for using enchanted items and potions (opens up a menu and pauses time), L opens up the journal, M opens up the local map, S shows your current status, R is what you use to rest, P activates pilfering mode, F1 looks at character stats, F2 tells you the coordinates of your current position, F3 does something with rolls that I'm not sure about, and F4 toggles pixelation.

thanks.. how do I use magic? I chose a ranger class but was told 'i am not a spellcaster'... can I not use any magic at all? is it possible to complete the game as a pure none magic user? (I avoid magic in all TES games)

It is possible to complete the game without magic. In Arena, classes are very important to what you're able to do. Your class will define which weapons you can use and whether or not you can cast spells.