how can I buy coins from a exchange without submitting my national Identity card or BVN number? As for those who did this how safe is it? I don't have anything against verification but I am not sure its safe or am I wrong about its safety?.
You can use some centralized exchanges that still have no-kyc tier with some limitations, for example Kucoin, but there is always a risk of your account being frozen and your coins confiscated for any reason.
To be fair, this could all happen with all other centralized exchanges even if you pass verification and send them all documents, or they can be hacked resulting in losing your coins.
Best thing you can do is using decentralized exchanges like Bisq, or P2P and face-to-face trading in your local area.
There are always risk with all trades, and all you can do is minimize it best you can.