The application keeps closing by itself, usually within 15 seconds or at the end of the game.

Happened to me a couple times this week.

Usually resolved itself within like 15 min though.

same problem, but for me the download does not want to start, it remains in the preparation phase and after 30 seconds it cancels itself .. this happens after I close the application when the download was at 15 gb, I cannot solve in any way, I tried all the solutions found on the web and I don't feel like formatting the pc for just one game.

If it's honestly beginning to be that much of a problem then I suggest you contact XBOX Support and setup a repair for your console. Anywhere from 10-15 seconds is well within reasonable startup times for most applications / games so please keep that in
mind. Of course as the XBOX 360 gets older in age the startup times go up in seconds not minutes of course. You haven't said how long it actually takes but if it's well within 30 seconds then that's really not that long in the grand scheme of things.

It usually connects itself at startup. And saying so, a message appears saying that it cannot connect, "please use the guide to connect".

Doing so, it should connect on the spot but it does not, a circle appears for close to 20 seconds and a message appears with a code (0x87DD000F)

It also disconnects itself sometimes saying something like "good by, hope to see you soon"

I'm running on 50mbs, 10 mbs upload and a ping of 15, sometimes going to 75.

If it's Xbox One games, it's a glitch that usually fixes itself within a few days.