Yes. Your game may read and write data to platform services and public third-party game services for player save state, identity, social graph, matchmaking, chat, notifications, achievements, leaderboards, advertising, player acquisition, in-game purchasing, analytics, and crash reporting.
Yes. You can use hardware you own and operate for your game. It’s also ok for your users to connect peer-to-peer, and for users to host personal servers (as long as they’re not operating as a service provider business).