Electrical – Outlets still have power but fuse is unscrewed

You need to trace the outlet back to the circuit breaker/fuse in the main panel and then see what amperage is carried by the circuit. Then you need to also find out what other outlets exist on the same circuit and what appliances are or can be plugged into them. If you overload a circuit (e.g. run your oven at the same time as running a circular saw out of a different outlet on the same circuit), the chances are the breaker will trip. That is less of an inconvenience than blowing a fuse that needs to be replaced. I am pretty sure that you use fuses and not breakers in your country but I may be wrong.

I guess none of really answered your question if it was common to have both breakers and fuses. I would not say it is common at this time but it is not uncommon for a house that was partially updated to have both. Years ago the code changed and we could no longer have rentals with fuses because of the fuse fire risk if oversized. A friend has quite a few rentals built in the 30's & 40's we did go in and replace the fuse boxes with mostly 100 amp panels on the houses that had gas heat and 150 amp panels with electric heat. These were all or mostly 2 bed 1 bath 900 square foot homes so these panels were close to 2x the size of the original fused mains. Of the 12-15 houses we updated I think 9 or 10 had mixed breakers and fuses, many of his other houses had been fully updated so in this specific case of homes in this era it was approx a 30% chance of a mix.