It may not be much help but when I tried looking up fuse values for sunroof I only found it for a US spec Fit/Jazz . And this had 2 fuses. a 7.5 amp one for the sunroof control unit and a 30 amp one for the sunroof motor.
Its not surprising the motor needs 30 amps. But 30 amps also requires a heavy duty switch. Cars normally minimise how much heavy 30 amp wiring is required ,and avoid hefty switches in the cockpit , by using a low amp switch and wires to operate a remotely located relay switch . (often located in fuse boxes) Relays are basically a heavy duty switch , which is switched on and off by a lower amp switch and wiring circuit.
Neither the relay or the motor itself should have worked at all if their respective fuse was missing.
I agree with Marco that the sunroof may either getting power from another source due to a short circuit, or possibly a previous owner tried to fix it by modifying wiring, connecting to another circuit etc. And if its intermittently getting power from both sources at the same time this may account for its erratic behaviour.
Sorry to say this but both scenarios could potentially be dangerous. And needs further investigation. If the motor is trying to draw 30amps through wire that is too thin the wire can overheat and cause a fire.
Faulty wiring ,switch or relay might also have added to the parasitic drain on your old battery and hastened the need for it to be replaced. The new battery may have changed behaviour a bit by providing more power . .