Woah. Germany has a lot of political parties, as a foreigner it can be kinda confusing. All of these parties hold some type of power?
Which parties are most comparable to the Democratic and Conservative parties of USA?
Imma need a ELI5 for German government cause I feel like an idiot.
No. As in many parliamentary democracies, after an election, parties either rule if they get an absolute majority of the seats (which very rarely happens) or several parties have to form a coalition. That means two or more parties who are close to each other get together to write down a "coalition treaty" with projects they agreed on to implement. Ministers are assigned more or less according to what every party wants (and how many seats they got in comparison to the other).
The chancellor will usually come from the stronger of the two parties, but there's no judicial necessity to do that. In principle, there's even a left-wing majority in the current parliament (SPD, Greens, and the Left, thus excluding the party with the most seats), but some of the Left's ideas make them more or less unfit for government, so they couldn't get together.
In terms of policies, it's a bit complicated. In some aspects, the CDU (the German conservatives, part of the current government and Merkel's party) are in line with the Democrats (e.g., universal health care, although the American version isn't (wasn't?) quite as universal as the German one; taking in refugees isn't universally loved, but they're more or less supporting Merkel's course), but in others, it's more around the Republicans (you probably won't get same-sex marriage with them). In general, though, the German conservatives are more left-leaning than the Republicans but do share some societal policies with them. They're catering far less to the, err, more nutty aspects of religious policies though. You won't find a single party in Germany supporting teaching magical stories about how the world came to be, and climate scepticism can only be found in the right-wing AfD.
Speaking of which, the AfD are a new party to the right of the conservatives (CDU). They're basically the more right-wing (and racist) part of the Republicans, but they're a little bit confused regarding how big they want their government to be. In general, though, they're more like the Front National in that they support a strong state with social safety nets and such. Except not for those pesky foreigners.
The SPD (social democrats, also part of the current government) are in general a bit to the left of the Democrats. The traditional workers' party, they lost a lot of trust when they invoked harsher rules for the unemployed. Again, American and European political systems cannot be compared 1:1, but the SPD under its current leader is probably what the Democrats would be with someone like Warren in the lead.
The Greens are the "ecological" party who pushed green energy when they were in charge (1998-2005). Traditionally an anti-war party, they nowadays are more in the realms of realpolitik (i.e, accepting that German military has some role to play on the world stage). They're probably the most left-leaning party in terms of societal order, e.g., the strongest supporters of LGBT rights or recreational drug usage. They got a bit marginalised in the last few state elections because their no. 1 topic was totally co-opted by Merkel -- she decided to get rid of nuclear power in favour of more green energy (well, at least in theory).
Finally, the FDP are traditional European liberalists, thus probably closest to the American idea of a small state. That also means, however, that they're the strongest voice in terms of restricting surveillance. They got voted out of the last parliament because they were seen as being mere stirrup holders for the CDU.