As far as cleaning masks for reuse goes: Hospitals used to reuse a lot of things, fabric masks and so on, but in recent history medical equipment has moved from reuse (with suitable cleaning) to single use disposable items. Hospitals used to have huge banks of autoclaves and staff that knew how to use them - now, I just don't know if they have anything more than the most minimal facilities for handling reusable surgical instruments.
On the subject of cleaning masks for home reuse, jury rigging an autoclave is a real practical possibility. Basically anyone that has a pressure cooker has an autoclave. Put some water in the bottom, put something suitable in as a shelf to keep items above the (boiling) water level. Put in items to be sterilised, close, run up to pressure, leave there 30 minutes (a pure guess, research needed), leave to cool down, decant sterile items.
When you stack up a proper autoclave you put items to be sterilised inside paper bags which are then sealed with specialised autoclave tape. Autoclave tape will withstand the heat and moisture, often has an indicator that shows whether it has been through an autoclave cycle, and seals the bag afterward, keeping the contents sterile. If jury rigging, masking tape might work. A typical lab autoclave cycle is anything from 30 minutes to overnight depending on what you're sterilising from a tray of small instruments up to 2 litre bottles full of culture medium.