I read that bitcoin wallet doesn't contain coins but keys, that the coins are stored in the blockchains does that mean bitcoin are not transferred(move) during transactions, but just a change in ownership?
Whenever you make a bitcoin transaction, you define a spending condition which is known as locking script and whoever can meet the defined condition will be owner of the coins.
The relationship between the private key, the public key and the address is a one way function I.e private key can't be gotten from public key, K= k*G where k= private key and K=public key and G=generator point, but saw something about brute forcing a two way connection wanted to know if brute forcing is impossible or just inefficient?
Any private key provides 128 bits of security and that's why brute-forcing a private key is practically impossible. In theory, it's always possible that you can brute-force a private key.