XnView should meet those requirements, as far as I can see.
Free and Open Source Software
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Am I committing faux pas recommending here something that's freeware but not open source? If not then Irfan View is great, see if you'll like it.
IrfanView (there's no space) is absolutely phenomenal!
yeah that's fine as long as they don't steal my data :)
Is Gwenview available for Windows? I quite like it on Linux.
DarkTable sort of works for that, though if I recall correctly the browsing is based on a "library folder" rather than freely browsing. It is very heavily focused around editing photographs.
My recommendation is to combine a decent image editor (eg. GIMP) with a good file manager with image preview.
The default image viewer in windows can do all of this
In Windows, the built-in Photos program(?) does most of what you want. Literally go to the folder where the images are, right click, choose "Open with" and then "Photos". It'll open the image in a very, very simple image viewer, where you can move back and forth between images in the same folder, and it has options for rotating, cropping, editing brightness, contrast, saturation, etc. The only thing missing is a mirror image option.
I use Photos pretty regularly, if all I need to do is crop or rotate an image, because its integration into Windows means it's significantly faster than opening a proper image editor. It's also really good for reviewing a whole batch of photos, as again its integration into Windows means you can delete an unwanted image within Photos and it'll remove it from the folder as well.
It's not open source, so maybe not quite what you're looking for, but it's definitely completely free and already part of Windows.