Is there a way to download apple tv content ( movies/shows) to my windows 11 PC from the browser?

You cannot. The https://tv.apple.com website does not allow downloads.

You can download the new Preview version of the Apple TV app for Windows from the Microsoft Store and use that to download content. click here ➜ Download the Apple TV Preview from the Microsoft Store

Note, that Apple warns that as a preview version it may still have issues and problems, and it will disable iTunes.

https://www.macrumors.com/2023/01/11/apple-music-tv-previews-microsoft-store/#:~:text=Last%20October%2C%20Microsoft%20announced%20that,for%20Windows%20app%20and%20Apple

Can you still do home sharing to an Apple TV box from your PC with the Apple TV app?