What coins do you mean? Can you name some?
Every real coin has a wallet, tokens have mother chains like ethereum or waves.
You can manage the tokens with the wallets from the mother chains.
This is correct. There is no coin that has no wallet. Even shitcoins have wallets. For the major ones that we have right now, these are mostly ERC20 tokens or coins which means they are using the Ethereum blockchain. Myetherwallet.com is the mother wallet for all of them. You can save them here because they are safe. You will have your private keys with you. There are also Waves-based tokens whose mother chain is using waveswallet.io. There is also a NXT wallet, Latium wallet, deeponion wallet, gravio wallet, etc.