You may want to see if there is a tax treaty between the United States and the country your father came from. If there is one, the tax treaty may tell you if the pension from the old country is taxable or not. If no tax treaty, my off the top answer is to report the pension checks received on the "Other Income" line. If there is an income tax paid to the country of origin on the pension, then the foreign tax paid may be used to offset all or part of the U.S. income tax., on a Form 1116.
As a general rule, 183 days of stay establishes residency or domicile in a state.