Get the Short Domain Name

CMD: echo %userdomain%

Powershell: gci env:userdomain

Get the Domain

From an elevated prompt (cmd or powershell)

nltest /parentdomain

Get Domain Controller

From an elevated prompt (cmd or powershell)

nltest /dsgetdc:<DOMAINNAME>

Ex: nltest /dsgetdc:foray.local

For other methods,

...

see: Find Name of the Active Directory Domain Controller.

Test Domain Membership (Trust Relationship)

netdom verify <Computer>

Ex: netdom verify MYPC

See also: Check Domain Trust Relationship