No, it is not possible to edit apex classes and triggers directly in production environment.
It needs to be done first in Developer edition or testing org or in Sandbox org. Then, to deploy it in production, a user with Author Apex permission must deploy the triggers and classes using deployment tools.
However, Visualforce pages can be created and edited in both sandbox and in production.
Only if the page has to do something unique (different values), it would have to be developed via Sandbox.