What position did the Church take on African-American slavery and the abolition thereof before and during the Civil War?

The Church condemned slavery well before the Civil War. In 1815 the Congress of Vienna, convened for the nations of Europe to negotiate and establish a lasting peace in the aftermath of the Napoleonic Wars, produced what is known as the Final Act as the culmination of all the different resolutions agreed upon at the Congress (you can read an English translation here). Among other things the Congress condemned the slave trade. Pope Pius VII was a signatory to the Act, and as far as I know it was the first official condemnation of slavery from the Papacy. This of course was not a view that permeated the Church as a whole-two of the largest slave-trading nations, Portugal and Spain, were also arguably the two most powerful European Catholic countries. Each protested the Chuch condemning the trade, and indeed some of the last places on the planet to outlaw slavery were Portuguese colonies.

Although Pius VII's signing of the Final Act was significant, I would argue that the real watershed moment for the Church in terms of opposition to slavery was the Papal bull (for simplicity's sake, think of the bulls like Papal proclamations) In supremo apostolatus, issued by Gregory XVI in 1839. Interestingly, the reaction in the USA hinged upon a translation of one line of Latin from the bull. The line reads "ne quis audeat in posterum Indos, Nigritas, seu alios hujusmodi homines injuste vexare", and at the time was translated "that no one hereafter may dare unjustly to molest Indians, negroes, or other men of this sort". The unjustly (which as of 1972 is no longer included in the official translation of the bull) was interpreted by some to mean that slavery was acceptable so long as the treatment of the slaves was not unjust. Of course this was less a difference in translation and more the easiest way to keep owning slaves without directly opposing the Pope. This becomes especially clear if you read the next two lines of the bull as well-ne quis audeat in posterum Indos, Nigritas, seu alios hujusmodi homines injuste vexare, aut spoliare suis bonis, aut in servitutem redigere ("that no one hereafter may dare...o spoil them of their goods; or to reduce them to slavery.

As far as the impact of the bull on the American slave trade, it was minimal. I believe the only state where it had any effect was Maryland (historically one of the most Catholic states, largely because of the comparative culture of tolerance there, thanks to its founder Cecil Calvert, 2nd Baron of Baltimore, who like his father before him dreamed of a haven for Catholics in the New World). Even there, the only real effect it had was on the Bishop of Charleston, who only interpreted the bull to condemn only large-scale slave-holding (despite, oddly, his own abolitionist beliefs) and to be therefore against the international slave trade, but not slavery itself. He even wrote several times to Martin van Buren's Secretary of State John Forsyth reassuring him that the Church was not condemning slavery.

It should be said that while I've laid out some of the views on slavery higher up in the Church, on the ground so to speak most Catholic orders in the early USA didn't have much of a problem with slavery. Notably, the Jesuits ran a plantation in Maryland which held hundreds of slaves until they eventually replaced their slaves with tenant farmers. They did this not out of remorse or spiritual motivation, but because the tenant farmers were more profitable-the slaves were sold away, not freed.

What role, if any, did Catholicism have in Southern/Confederate society?

Two slave-holding states had major Catholic populations: Maryland, as I've mentioned, and Louisiana which had originally been a French colony which still retained (and still does) a lot of cultural differences handed down from the French. Although other Southern states had Catholic populations in no other state did the Church hold the kind of power it did in those two; many in fact had significant numbers of anti-Catholic Protestants (which is not to say that all Protestants, then or now, are anti-Catholic). Catholicism in the USA overall didn't really begin to increase in proportion until the 1840's or so with the influx of Italian and Irish immigrants, but they settled almost exclusively in Northern, industrialized states (i.e. in Free States). The Confederacy tried to establish relations with the Vatican during the Civil War, with Jefferson Davis sending Patrick Lynch, bishop of Charleston (not the one who wrote the letters) as delegate to the Holy See. The Vatican however refused to recognize the Confederacy, and the Pope only received Lynch in his capacity as a bishop.

Overall it's hard to argue that Catholicism had much impact on Southern or Confederate society (i.e. on the South before the war or during), largely due to the fact that only two slave-holding states had major Catholic populations. It must be said that Louisiana was notable for a higher proportion of freed slaves and for having more educated freedmen than its Protestant neighbors. The New Orleans parish was actually unsegregated, and is home to the only Catholic historically black university (Xavier) in the USA.

Of note is the strong strain of anti-Catholicism in many parts of the South before the conflict-when southern Protestants were often enraged by northern Catholic abolitionists, especially those of Irish descent, during the conflict-when many accused all Catholics of secretly holding abolitionist tendencies, and afterwards-when groups like the KKK harassed and killed Catholics as well as African-Americans. A lot of anti-Catholicism sprung from hysteria about the influx of Irish, Italian and German Catholic immigrants. Indeed, many northern Catholics were fervent abolitionists, and the Irish in particular were notably over-represented in the Union Army.

What role did the Church play in the later Civil Rights struggle?

Sorry I can't give you more about this, it's not an area I'm very familiar with and while I could maybe cobble together more from Wikipedia I don't want to engage with something I'm not versed in enough to avoid mistakes. I did just read an interesting article on this, that I'd recommend if you have JSTOR access.

The Catholic Church had a varied role in the Civil Rights movement. On the one hand, most bishops in the South refused to condemn segregation. The Church abided by Jim Crow laws in Southern states and built separate churches for black and white Catholics. Martin Luther King's famous Letters From Birmingham Jail was a response to A Call For Unity, written and signed by eight local (white) clergymen, including the auxiliary bishop of the Mobile diocese (auxiliary bishops are extra bishops for dioceses where the extant bishop either can't perform their duties or have so many people that they need help with them, basically). On the other hand, many nuns and priests individually marched in civil rights protests or otherwise engaged in the movement. Here are some images.

Anyway, hope that was helpful! Sorry I couldn't give you more about the Civil Rights movement, and let me know if you have any questions.