A) Germany has a (predominantly) proportional system, but parties get in on list votes only if they pass 5%. Seing its poll numbers sink, FDP campaigned for CDU voters to give their list vote to the FDP - maybe with overwhelming success.

B) Last night, popular German talk-show host Stefan Raab did his own election show. I don't have a very high opinion of him, yet he is very popuzlar among a certain section of the youth. Meanwhile, in recent years, the FDP has tried to attract just this clientele. Yesterday, in the show, they held a mock telephone voting of viewers, and the FDP of course did rather well. Maybe this had a lasting effect on some young people who would have voted for CDU.

C) IMO most likely: on the TV channel ARD, polls showed a dramatic swing in preferred coalitions: the popularity of a CDU/SPD Grand Coalition slumped, that of a CDU/FDP one rose. Maybe a lot of CDU voters wanted to prevent a Grand Coalition.

_{*Lunatic*, n.
One whose delusions are out of fashion.}

Nothing written of course. :)
But there was always the public assumption that this would be the "natural" coalition.

Or could the SPD, the FDP and the Green Party go altogether into a Coalition?

In principle yes. It happened in states already.
But on the federal level there are "tensions" - to say it politely - between the Greens and the FDP.

How do you interpret that the FDP had such an increase in votes? Isn't that just to show that there are a lot of people, who are unsatisfied with either SPD or CDU and for lack of an alternative they voted FDP, because there wasn't anything else for them to show their discontent?

I think nobody right now can really interpret the results. Certainly not the pollsters. :)
But personally I don´t think it were dissatisfied voters. Looks more like people were assuming that the CDU was safely above 40% and giving their "second vote" to the FDP to bolster them. Kind of tactical voting.

I really, really don´t like this result!
It´s either a big coalition or some sort of three party coalition.