Xbox One and Xbox 360 same account

Yes and no. Your microsoft account can be signed in to both a Xbox 360 and a Xbox One at the same time, without any issues.

As a secondary issue you face, it is against the terms of service to share your xbox account with another person. While I am personally doubtful that Microsoft would act against you, you should be aware that using differant WiFi connections suggests access from differant IP addresses, which in turn could raise a red flag.