Can you continue to play from xbox one on the new xbox with your old profile?
Clear. That has nothing to do with the hardware.
Of course. The "Xbox Live" network will continue to be used and will therefore also be available on the new one. Similar to the jump from 360 to ONE.
Naturally! That was also the case from Xbox 360 to Xbox One. This would be almost illogical. You can even use your Xbox account on the Windows 10 PC, and even a number of games on Android (for example Minecraft) can be used with the account.