where is recommended to keep coins safe and get some incomes/profits from them?
If you are looking for a service gives you interest, there is no secure option for you.
For getting interest, you have to give your coins to a third party.
Exchange servers or on cold/warm wallets?
An exchange (as is name suggests) should be using for exchanging your coin. You shouldn't use an exchange for holding your funds.
With using an exchange, you give a third party full control over your fund.
About wallets:
It's always recommended to use cold wallets. It can be a hardware wallet or a paper wallet.
Note that if you want to use a software as a cold wallet, you should generate the private keys (or the seed phrase) on airgapped device and your private keys (and your seed phrase) should never touch the internet.
If you want to spend your coins on every day, a cold wallet may not be good option. But note you still need to make sure that the wallet has been created on a secure device.
A good wallet which I can recommend to you is eletrum. It's an open-source wallet which gives you full control over your fund. Electrum can be used as a cold wallet and a hot wallet.
if wallets which one is trustworthy Atomic wallet, Exodus or..?
Both Atomic wallet and Exodus are close-source and we don't what's happening behind the scene.
It's possible that they have access to our private keys.