I’m an American citizen and my fiancé lives in Bethlehem, Palestine. I’m going to visit him and his family on September of this year. I want to spend one month with them. Is it possible to take a flight one way and then buy a flight home when I'm ready to return to America?
Your problem is with the airline letting you on the flight, not the border guard, although the border guard will be very interested in your travel to Palestine. However, if you are refused entry at the border, it will be for "security" and not over a ticket.
In theory, a return or onward ticket is required. In practice, over a couple years, only British Airways enforced the rule and did not let me board without one. Air Canada, TWA (now defunct, of course), and Lufthansa did not, perhaps others. (Eventually I had a work visa which made the issue irrelevant.)
Assuming you have some money on your credit card, do what I did. Be prepared to buy an expensive, fully-refundable return one-way ticket. And then, once in Israel, cash it in for the refund. British tried a rather interesting gimmick of selling me the ticket in GB pounds and refunding the same number in US dollars, but the credit card company helped me set them straight.
Gratuitous advice: also be prepared for a lengthy exit interview, including search, when leaving Israel, because of your personal connection to a Palestinian.