Is there any way the Papal States could of united Italy in the mid to late 1800s? If so, how does this affect the Catholic Church, and will Italy still set up colonies in Africa?
a) Yes.
b) A less militant Catholicism, the Catholic church remains a prominent player in society and politics, an even less industrialized Italy (the Papacy was notoriously against even basic industrial standards such as railways in the 19th century); I could go on but you should get the idea.
Religiously speaking there's likely no
Rerum Novarum; hell Americanism might be out-right declared a major heresy, likely leading to a split in the American and European Catholic churches. An Anti-Pope in Baltimore is entirely possible, and/or a Neo-Pelagianit doctrine might arise in the states.
c) Most likely, though under very different circumstances, and likely to a much lesser extent both in size and scope. Papal Italy might very well try to 'reconnect' with her 'lost sister' in Christian Ethiopia.