I want to be clear that trust Wallet and Bread Wallet are non-custodial wallet ?
Yes, both are non-custodial(at least them claim to be).
Is it safe to store bitcoins and crypto in these wallets because we have full control over the private ki ?
Yes, I personally have used BRD as a hot wallet and it's pretty decent. But of course, with bigger amounts of funds, a hardware wallet is the way to go.
In case, both of them close their services, we can still use our coins by importing private key in other wallets ?
With BRD, yes. Not sure about Trust wallet, but most likely yes.