Yes and No. In Iowa, you must be a member of a political party (currently: Republican and Democratic) to vote in a primary election. However, anyone* can change parties on Election Day and vote. For independents to vote they must declare a political party.

*Precinct election officials may not change political parties within 30 days of an election.

Yes. Any eligible voter in Iowa may register to vote. Because many of those who are homeless have a nontraditional address they just need to provide an address or description of where they sleep the most, wherever that may be.