1) If a phone service provider you are using in office allow you to deflect of forward an incoming call to other number, then yes, the call may be forwarded to other number including your home one. It may cost something or may be free. No one external can tell you what your office PBX support/allow nor if it will cost something. Ask administrator of your's phone system.
1b) "transfer call to" is about destination. "so it seems as you are in" is about source. I see no relationship between those two parts of question, so I'm not sure I understand your's question at all. Are you wishing to call someone from your home phone, but you wish an office phone number will be displayed on called phone instead ? For direct call it depend on your home phone provider. For call passed thru office equipment it depend on capabilities of such equipment. Ask either your home provider or administrator of office's phone system.
Sorry, there are no generic answers to your questions.