Welcome to Just Answer!
The zip line needs to be taught if it is close to level, not counter weighted on one end.... that puts way too many variables on the operation of the chair... just stretch it taught if you are tied near the base of each tree... so that the center sags from a straight line in the center by 1 to 2 meters, try it at 2 meters first, put a dead weight in the chair and run the chair down the zip line, if it is a stable smooth slide, leave it that way... if there is a bit too much bounce in it, tighten the zip line up a bit.
The higher the start end is from the finish end, the more sag there needs to be in the line so that the terminal speed at the far end is not too fast for the person in the chair to handle... you adjust the sag to regulate that speed.. it is a trial and error approach... try it with a full range of weights in the chair.
Tell me what tension the 12mm wire is rated at, If you are running 100kg loads, you will want the wire rated at 400kg. PLUS the weight of the cable itself. thats a generally accepted structural design parameter.
The other factor is movement of the trees in a wind storm and how that will affect your line. Tell me the diameter of the tree trunks, how far above the base of the tree you attaching the line and what the straight line down slope is.
tie the line around each tree, with at least a 2 inch wide x 1/8" thick metal saddle so that the wire does not cut into the tree...you can have a weld shop attach come loops to hold the wire to the center of the metal band.
Let me know if this makes any sense on your end, and answer my questions... we can go from there until you have the full and complete answer you need.
I am off to bed shortly, if I miss you tonight we can pick this up again in the morning.