When you think something is wrong it probably is!! You have pointed out several things that did catch my attention. The "strap" on the bed for one. That is not good. Restraining someone with dementia only creates agitation and the stress involved will make them deteriorate quickly. Stress is NOT a friend of dementia. In solving a night wandering problem in this way you only make everything else worse. We always talk about not arguing with a dementia and not saying no... restraints are a non verbal argument and saying no in a huge way. I would be investigating why it is there and how it is used.
The rearranging of the furniture, like you said, is a huge clue. Routine is necessary for dementia. Simply changing a picture on a wall will throw them off. Rearranging all the furniture may be why she doesn't think she is in her home. Changing a bed spread is bad enough. I remember a night when Dad insisted that Mom was in somebody else bed. He was FURIOUS! She was cheating and he caught her!! Humm... the comforter that belonged on their bed was missing. He didn't recognize the bed at all!! The bed was blue and not white. Later I realized that when he threw off the blue spread onto the floor in anger and the white sheet was exposed... he calmed down and went to bed. The little things DO make a huge difference with them.
How many hours does this lady work? Is she a 6 day live in? Is Mom at home with the one brother at night? Is there somebody there all the time?
Not recognizing people she should know is common as the disease progresses. It may come and go for a while and eventually become an all the time thing. Dad thought sister 3 was my aunt. Mom has talked to me about Deb as if I was not there. She has mistaken staff as her grand daughters but not recognized her grand daughters when they came to visit. We have to remember that our loved ones may be in a different time when they look at us. Mom may not recognize me as a slightly gray older lady but remember me as a toddler that she is putting in time out. Dad may look at my sister (who does look like my aunt) and think he is looking at his sister long ago. If there are changes in the house she may not recognize it as home, or she may be looking for the home of her childhood. You never really know. What you do know is that it is real to her and you just have to go with it.
Wandering is a huge problem. They may have never wandered before but that doesn't mean it won't happen. Dad had degenerative back disease and arthritic knees. He was not a walker.... but he managed to wander off a few times. When they get a thought in their mind and a determination in their step it is amazing what they can do.
If you think something is wrong then get nosy. Be more present and see if you can figure out just what is going on. Dig round of evidence that there is bad food there or things put in odd places. Mark the shampoo bottle levels and see if they get used at all. Count the towels and come back tomorrow. It is better to know than not to guess
Vigilance and an open mind to the possibilities will pay off.
Until then keep venting and questioning......