This part of a double hung window sash called

It's a window latch and keeper. Unscrew a good one, head over the your local hardware store, and see if they have a match in stock. Pay close attention to the distance between the screw holes and the how tight the two parts are pulled together. They come in a lot of styles, e.g. this would work if the keeper was on a horizontal instead of on a vertical surface:

You can also look online, and worst case scenario, you'll have to go to the window manufacturer to get the replacement parts.

You're not allowed to install blinds or curtains, are you allowed to apply anything to the glass?

In order of most realistic to least I would suggest

• Applying a reflective coating / thin film to the windows, such as is used in one way glass, I believe a consumer grade version of this can be purchased on a roll and may be made of mylar or some similar non-reactive plastic
• Place a decorative room divider such as these between the window and the line of sight you wish to block. You'll still get good light transfer during the day time but more privacy at night.
• Using masking tape, painter's tape or some other easily removed solution, tape either a lightweight fabric or decorative paper over the windows. It ruins your enjoyment of the window, but gives you the privacy you want

Barring any of these solutions ask the land lord for ideas, since they've likely dealt with it at this location before.