Removing Alarms & Clock App and Bing News is likely to impact Cortana ability to set reminders and bring you stories. In general, removing Microsoft Apps is not going to impact the functionality of your Windows 10 computer in a major way. Note: Apps like Cortana, Edge, Windows Feedback, Contact Support, Xbox cannot be removed.
However, it is possible to delete most in-built Microsoft Apps using Command Prompt or PowerShell Commands.