Trying to identify some very old Magura rim brakes
Magura hydraulic rim brakes are a quality product. They still make these and many of the older models are sought-after in the retro mountain bike scene. They are durable and perform very well. From your pictures it seems you have direct mounts on your frame specifically for these brakes, this is now most common on trials bikes.

The brake pad fitting is the same throughout the range, many 3rd party manufacturers produce replacement pads for these brakes and they're no more expensive than other brake pads. Kool Stop, Kashimax and many others are widely available. Google for "Magura Rim Brake Pads"

To remove the pads, remove the wheel and pull them out of the holder. To replace, just push them into the holder. It's that simple.

They may also benefit from being bled and having the fluid replaced. Bleeding and re-filling sounds daunting but it is possible to do at home and the kit is usually inexpensive. Youtube has many videos detailing the process.

Overall, these are good brakes and barring mechanical failure, they should provide you with many more miles of trouble-free usage and good performance.