Exchanges should be treated like a market place where you are to on buy and sell crypto. Exchanges are poor ways to store your crypto, because you are not the righful one in control of your private keys and you can lose your coins any time. We have seen stories of exchange hacks and exit scam.

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- Which hardware wallets or apps do you recommend? 
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Hardware wallet is good because the seed are always offline. Trezor is a good hardware wallet for multicoins storage, you should check it out.