Re: paying with strike — yea, if that’s the payment method you chose, then that’s how you would send fiat to your trading partner.

If by safe you mean private, then yes, relatively so. There’s no public correlation of your fiat spend to your Bitcoin stack. Of course Strike knows you sent money to someone, and that person knows of the trade, but its far safer than a centralized exchange which can be leaked/hacked and tell the whole world of criminals that you have a fat stack of sats and make a good target for home invasion and robbery.

If by safe you mean “avoid scammers” then yes, again, relatively so. The escrow system punished bad actors and it seems to do a decent job on that.

To go from Alby to cold storage, anything swapping service that offers Lightning and on-chain would do the trick. Aqua Wallet, Boltz, Flyp.me all seem pretty solid