If you use Bitcoin Core or a wallet like that (that saves a wallet.dat file with all the private/public keys) remember that each time you generate a new key, your last backup will not have this key. Since it's recommended to generate a new key for each transaction
Absolute nonsense. Bitcoin core pre-generates 100 addresses and private keys for you so that when you request a new address it can just choose from the pool of already backed up keys. If a pool of 100 isn't enough, you can increase the size of the pool to as many keys as you like. Please, take your signature spam elsewhere.