Need Help Modernizing Bathroom Basement...

I have a full bathroom in my basement where I'd like to install an exhaust fan. It's basically a toilet, sink and shower with no stall. Also, it's unfinished -- just painted masonry and a wooden door. It's about a 5 x 7 foot space. Also it has the original 1950's ceiling tiles (some sort of acoustical fiber board, stapled to the joists -- they have a pattern of holes).
Can the fan vent through the window or does it need a dedicated exhaust? Also, should the ceiling go? I'm not sure what the material is or if it's humidity proof (I'm guessing not). Any other ideas?
Thanks in advance.
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
Add image file
Upload is a website for homeowners and building and maintenance pros. It is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.