Can I charge a 12V/4Ah sealed rechargeable battery with a 13.5V/500mA charger? If so, how much time would I need to charge it to 100%? If not, how can I charge the battery?
A lead-acid battery labeled 12V, 4Ah and a lead-acid charger labeled 13.5V, 0.5A can work together, likely. Lead-acid manufacturers prescribe that the battery should not be charged at a rate greater than C/3. A 0.5A charge going into a 4A battery is C/8. Expect that it would charge in 8 hours.
Nevertheless, take precautions. Charge the battery outside at least first few times. Lead-acid batteries (abuse-tolerant that they are) can vent hydrogen when abused.
Further reading: BU-403: Charging Lead Acid