what happens at registered domain .com in trial if i decide to close account?
You get to keep the domain, as you've already paid for it. (You were charged $9.95 at the time of signup to cover that.)
but if i close my account, how can i manage my dns domain?
You can still log into the panel when your account is closed. You lose access to the hosting features of the panel (like creating users and hosting domains), but you can still manage your domain registrations.
And you can always transfer your domain to any other domain registrar, though we'd be sad to see you go.