The complexity and length of the private key determine how feasible it is for an interloper to carry out a brute force attack and try out different keys until the right one is found. Please does this mean that the private key isn't 100% secure since interlopers can carry out attacks on wallet.
It means the longer the bit of the private key, the more harder you will try to brute force it. The present ones are 256 bits, the size of bitcoin’s private key space, (2^256) is an unfathomably large number. It is approximately 10^77 in decimal. For comparison, the visible universe is estimated to contain 10^80 atoms. Reversing the elliptic curve calculation is impossible, while the present day technology can not brute force such large number as 10^77. Also, the brute force you meant here is when the public key is revealed and used to brute force the private key, not yet when the address is reveal which is now what public should know. If only the address is known, this will be more difficult. I do not want to go much depper into this. But, just know private keys are 100% safe, only what makes them not safe is when you reveal your seed phrase or the private key to another person, it can also be revealed through malware attack on devices.
https://github.com/bitcoinbook/bitcoinbook/blob/develop/ch04.asciidoc#base58Encryption key management can become too complex if each user has their own private key.
Encryption is not necessary, private key is safe but just for additional protection, and it is optional.
Private keys need to be changed frequently to avoid being leaked or stolen.
No, protecting it is right word here.
If the private key is forgotten or lost, the system is broken and messages stay encrypted.
Does this mean once a private key is stolen or lost it can never be recovered?
If the private key is known to another person, the person will use it to access the bitcoin the private key controls and used it to unlock the bitcoin on blockchain.
Significant computing resources are required to create long, strong private keys.
HD wallets is enough for this.
The private key cannot be changed, each Bitcoin address you own is represented by a different Private Key. What does this mean? You are not allowed to reveal your Private Key under any circumstances. If you lose the Private Key, you have lost all Bitcoin in that address.
Yes, you are right. But private key does not represent addresses, but private key generates digital signature used to unlock funds stored on blockchain through public key using a digital fingerprint called addresses.
Yes, the Private Key is the most important factor in keeping your money safe. It cannot be recovered.
You are also right, but we should also mention
send seed phrase as very important, it can generate the private key which means it should be protected like private key, any access to seed phrase also means the private keys can also be accessed and can lead to coin lost.