Bathrooms at these kinds of places (old psychiatric hospitals) usually have little or no privacy, and are typically smaller. It's difficult to say what the room could have been used for, as there is barely anything remaining. It could be an area where routine examinations would take place, or some service like washing bedpans, or an infirmary.
It's like a mitten without a place for your thumb, usually made of a strong nylon material. They prevent someone from hurting themselves or others by scratching, picking, etc. It could suppress habitual behavior or simply to stop one from picking out their stitches after surgery.
Often, used and/or old medical equipment from hospitals, etc. cannot be easily reused once the facility shuts down, especially if it was a state owned facility - unless the regulations of that state allow it to be recertfied for other use. This usually applies to sophisticated electrical or electronic equipment such as x-ray machines, etc., which often have aged to the point where it isn't worth the repair/upkeep costs to get them recertified, if they can be recertified at all once moved. At some point equipment is just too old to be used anymore. This shouldn't apply to implements like pictured here, as age does not really affect them, but regulations for use apply to them as well. Part of the problem is there doesn't seem to be much of a market for old medical tools. A state just can't give taxpayer owned items away without legislative action, and I'd imagine if there a big demand for these implements some bright entrepreneur would have petitioned the state to purchase them for resell. Perhaps someone will. Shame for them to just sit.
Yeah, thanks Iceberg - sigh - caretaker nursing down on knees, outside doors, all along the hallway - the things we Human Beings dream up + invent is ludicrous + risible at times. Imagine it.