Is it possible to control my light and ceiling fan using both wall switches and a remote?
Lutron has an answer to your question

As it turns out, Lutron, at the time of this writing, has just introduced a fan control into their line of Caseta wallbox/remote capable controls.  I would use two Caseta controls side by side; namely, a PD-FSQN and a PD-5NE.  Note that they both require a neutral wire at the switch box to work (which may or may not be an issue with your wiring, we'd need photos of the inside of the switch box to know for sure), and rely on wall-mounting hand-held remotes (Caseta controls use Lutron Pico remotes) for multi-way control, if that is acceptable for your application.