Foreign tax credit when filing a dual status return

I moved to the US in June last year. 
Can I file my return as dual status (resident June onwards and non-resident Jan to May) even if I am a non-resident in my home country (June onwards).

Basically does residency in the country I come from have any impact on whether I can file as a dual status return or not in the US ?

Also, while filing as a dual status alien, for the time I am a resident in the US, if I had income sourced in my home country which was taxed by the US as well, can I claim foreign tax credit on that to reduce my US tax liability ?