These sound like a lot of the problems I used to get with the original OS on the XB1 from two years ago. Mainly it's not surprising to hear the issues with the MCC, that game still has problems to this day no matter what any apologists wants to say and works like some infection. Doesn't work well when switching between apps, especially party chat and causes lots of problems.
I have had those issues with Halo 5 numerous times, from the game refusing to connect to online from the main menu to booting me from matchmaking, to reqs never appearing. Game can be a total shit show requiring a hard reboot. However all these party drops outs sounds more like a connection issue, you may want to hard reset the console than manually reconnect it to the internet, for whatever reason that fixes issues I have come across.
Installations I have experienced that too but mainly because I'm in the preview and with the Movies and TV app, which recently as decided that it's file size is infinite, usually restarting the download helps with that. I will say that is really, really rare for a problem so don't expect that to be a big issue.
Store is slow and laggy as shit, truth be told it's actually better than what it was but recently it may be getting worse. That's the XB1's biggest issue.
Try plugging the console right into the wall, for whatever reason even the instructions say this, a lot of problems come from plugging into a power bar. The system has its own short circuit protection, now I don't do this but a bunch of XB1 users from the subreddit swear by it. Up to you.
If it's still a shit show after any kind of fixes I or anyone else mentioned just returned the bastard.