using three major algorithms (Private keys, Public Keys and a signature).
This is one "algorithm" called elliptic curve cryptography. The 3 you mentioned are the components.
Bitcoin specifically uses Elliptic Curve Digital Signature (ECDSA) more specifically "secp256k1"
Secp256k1 is the name of the curve that bitcoin uses not the algorithm.
Bitcoin also uses ECSDSA (Schnorr signatures) after Taproot activation.
what this means in essence is that it is difficult to break this algorithm by performing 2128 symmetric-key cryptographic operations such as invoking a hash function.
It has nothing to do with hash function and the algorithm is referred to as asymmetric cryptography not symmetric and also the security is calculated based on the solutions for ECDLP.
ECDSA is a good tool for randomness because it makes guessing the private key from it's corresponding public key difficult and impossible.
Not being able to reverse the private key to public key operation has nothing to do with ECDSA which is the digital signature algorithm.
It can take a message of 256 bits long and this doesn't limit the amount of messages it takes has input because messages get hashed before they get signed which means any size of message can be efficiently signed.
That's a weird sentence. The "message" can have arbitrary length, the hash used in signing is 256 bit.