I wanted to use itch. io for my thesis experiments and having the game in a browser would be ideal. However I need to run some in game analytics and I need the player to send me this information. Is there any way to do this with a browser game?

what game engine are you planing to use? I would imagine the skills needed for this would require specific coding skills and possibly data management, but I believe it’s possible.

You might want to look into the Score Space game jam Discord server, those developers specialize in online leaderboard integration 

Answering your question in the title, Yes.

On one page you can upload different files, only one can be playable on the web, but the rest can be left for download, you just need them to have different names.