Only US citizens may depart the US for extended periods and return to recommence an open ended residence. While permanent residents may travel internationally, they must retain their intention to maintain their primary residence in the US. Demonstration of this intention may be undermined by extended absences abroad, purchase of residence property in another country, or taking foreign employment, for example. It is not sufficient to simply return to the US once a year. Permanent residents anticipating an extended absence from the US of up to two years may secure a reentry permit which preserves status while away and may be used to reenter on return.
Yes, but you must obtain advance parole from USCIS before leaving the country, which is liberally granted. Leaving the US during an adjustment of status is deemed a withdrawal of the petition requiring the process to start over again.