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1) for each private key there is only 1 point (n private keys, n points, n is the order of the curve)
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I know that EC collision is not proved as there is no example.
Yes, for each private key there is only 1 point, however not necessary that if we have n private key we will have n different points.
Simple example for the group of 10 elements:
Key Point
1 7
2 6
3 5
4 7
5 3
6 2
7 7
8 0
9 9
0 7
You can see that for each key (0..9) there is only one Point, i.e. we do not receive 2 or 3 or more points for each key. We have only one point. However key 1,4,7 and 0 lead to Point 7 (collision). For group of 10 elements it is easy to check.
However how could you be sure that for group with almost 2^256 elements for every private key we have the unique Point?