This means if you use an HD wallet, you can eliminate the risky effect of the change address generation, because your change addresses are already generated and stored in the HD wallet itself? So if you don't spend the whole amount of the unspent output, the change will remain in your own wallet, just on the next address, and you won't need to remember the private keys, because your seed will regenerate your HD wallet anytime you need and you will have the control all of the addresses.
Yes, that is all correct. That is why HD wallets became very popular quickly after they were introduced.
Does this also mean that if you use a paper wallet, you need to import the private key into an HD wallet, not to lose bitcoins because of random generated change addresses?
That depends on the wallet.
For example, Electrum 2.0 and later has a "sweep" function, which sends all bitcoins (less the transaction fee) in a private key (that you copy from a paper wallet) to the next address generated from the seed key.
Mycelium can import a private key (scanned from a paper wallet) into an "unrelated account", that is separate from its "Bitcoin HD" account. I don't (yet) know where the change goes when you spend from a unrelated account.
All the recommendations I have seen say to always send the entire amount when sending from a paper wallet, to avoid issues with the change address.