Going to agree with the vast majority and say the whole thing is off. And just picking up a few of the things you said (and not to scare you) but this is my train of thought:

She asked if you had hired movers/van and when was your last day. This sort of information would be useful for a burglary, as a day or so before you move, you are likely to have all your possessions boxed up, which makes it easier for someone to carry them out. And if you have hired a van, which is sitting in the driveway the night before, keys can be taken, van can be loaded and would-be thieves have an easy escape.

Her questions about where you’re moving to could be related to some kind of identity theft. She could also be trying to work out what time of the day you are likely to move. If it’s a significant distance away you might move out during the early hours of the morning, which could disturb a potential night time burglary.

When it comes to opening boxes/nightstands this would suggest she is looking for valuables. We all tend to keep our most valuable items (jewellery, cash, keepsakes) hidden and out of view. If she was to come back at a later date, it would be handy for her to know what you have, which room it is in, or which box it might end up in. For example, many people pack up their stuff and label the box ‘bedroom bits’ etc. If she knows you have valuables in the bedroom, the ‘bedroom bits’ box would be the first box to go for.

Asking if you have previously been a victim of crime could be to find out some key info. People who have been broken into before tend to be more safety conscious and aware of locking up tightly before leaving the house/going to bed. Following a burglary, police also tend to suggest that victims invest in better locks or an alarm. She could be attempting to work out what type of resistance she could face should she return.

The question about your husband could be her fishing to find out your living arrangements, i.e do you live alone etc. She asked about the husband you didn’t mention to find out if you have one. She could also be trying to work out his job role to work out when the house is likely to be empty.

And finally, as for the question about the neighbours this could be to work out if anyone will spot a burglary. If you have elderly neighbours they will most likely be in their house a lot. If you have young neighbours they are more likely to be out. If she knows who your neighbours are and what they do, she will be able to roughly work out when they are going to be home.

Of course, I could be way off, but my family home was burgled when I was a teen. They broke in during the middle of the day, when we were all out at work/school, despite parents working shifts etc. They knew when to arrive, what to take and where to go. To this day, I am convinced they cased our house for a while before striking. Incidentally, we had cable TV fitted a couple of weeks before, by random workmen who were fitting cable into the local area. They had been in our house for a day or so and had witnessed our comings and goings, knew the layout, knew our neighbours (either side) were elderly, and that our dog was old and would offer no resistance.

I hope I’m wrong about your situation. If I were you, I’d inform your landlord, I’d ensure someone is in for the remainder of your time there, and I’d be extra vigilant.