A wallet is a collection of Bitcoin addresses and it contains the private keys (unless it is a watch-only wallet). People normally encrypt the wallet file to protect it. If you had a copy of that wallet file you could try to break the encryption. That depends on the type of encryption, length of password, etc. there are services that crack these wallets and I assume they use tools like John the Ripper.
If you see a Bitcoin address on the blockchain and you try to find the private key randomly most likely the sun will burn out before you find it.
I can't make heads or tails of the part about the mining difficulty of different proof of work algorithms. ASIC miners can only do hashes, they can't generate Bitcoin addresses if that is what you mean:
https://en.bitcoin.it/wiki/Technical_background_of_version_1_Bitcoin_addresses