1. Best and secure wallet to store for different coins(I heard that coinbase is too expensive to withdraw the coin)
If you want to store coins, then do not use wallet in an exchange. Better to use wallet which gives you a full control over your coin, for bitcoin then I suggest electrum and mycelium.
2. Without verification of ID, can deposit/withdrawl money from coinbase
Most big exchanges requires KYC, why do you worry about KYC in an exchange? Indeed there are some exchange lets you to trade without KYC (mostly centralized exchange). Do search on google and you may find some alternatives.
3. Secure exchange for trading with USDT (no need for id verification when withdraw the money or coin)
4. Do you have good experience with Kucoin and yobit?
Kucoin lets you to withdraw 2BTC/24hours without ID verification if I remember it correctly and I think it is a lot better than yobit.