Is it possible without the private key to divide a point by 2 ?
why not. private key will tell you how many times to add G to itself. but after you are done and have the value for k*G as point P then you can do whatever you want with that point. for example you can add another G to that point and compute Q=P+G or R=P-G and similarly you can multiply that point with any number like computing S=3*P (the same way you would compute 3*G).
2
-1 is just another number that your point (P or G or Q,...) is multiplied by. you just have to first calculate what integer 2
-1 is in congruence with. to do that you compute its modular multiplicative inverse as i explained above. there is also an example in my second comment with small numbers.