Do you use emerging cryptocurrency exchanges? What are your thoughts on trusting these smaller exchanges? Additionally, some of these exchanges host events where we can earn altcoins. What do you think about such events?
I don't trust any centralized exchange, not to mention new ones. New and smaller exchanges are riskier, even for trading, older centralized exchanges may be okay for trading, but neither of them is recommended to store your funds.
Is a platform that uses cold vault reliable in this regard?
A centralized exchange isn't going to help your store all of your money in cold storage, they make more money through fractional reserve, so your money is risked in one investment or the other. They also have to store part of it in a hot wallet, where it is easily accessible. Don't deceive yourself, your funds is only safe in your own self custody, buy a hardware wallet or set up an airgapped wallet yourself, that way you are sure of your own security.