How many languages do each of the members speak?

Bjorn can speak French
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Agnetha and Bjorn seem to be able to speak German pretty well.

Frida replies only in Swedish in this interview.

In the clip below, both Agnetha and Frida speak German well, albeit that the jokes seem to be rehearsed. Agnetha lived in Germany for a year or two pre-ABBA.

 

The first clip is a 1976 interview in English, but for the German tv show Musikladen. After confirming that the group do not all live together in the same house, Agnetha says 'thank God' in German, apparently spontaneously. The second clip is from 2013. Agnetha still speaks a little German with a good accent.

^^ Whereas Norwegian and Swedish are two separate languages that can nevertheless be mutually intelligible, the Swiss German spoken in Zermatt is apparently the opposite: a dialect rather than a language, but Germans cannot understand it and require subtitles! Kids learn something else called 'Swiss Standard German' too, as if French, Italian and English isn't enough of a handful already.

My German is very rusty, but even I can pick up too much of the Zermatt 2017 interviewer's questions for it to be Swiss German.  I can't understand the guy with Frida, but he may nevertheless also be speaking German with a strong local accent, rather than Swiss German. Do we have any native German or Swiss ABBAchatters?

When he first greets Frida, I can't make out whether she replies in German or English; the 'hallo' would work in both languages and I can't hear what else she says. She appears to understand his first question in German, although there is an edit just before it, so he may have prepared her. In all of her many Zermatt YouTube clips for German/Swiss tv, including this most recent one, I can't find any in which she doesn't speak English throughout.

The German prince that Frida married had a Swedish mother and was educated in Sweden. Also, his first wife was Norwegian. So Frida may not have needed to speak much German, and may not even want to, given the parental history thing. As for the Swiss German dialect spoken where she lives, it could only really be used with a few thousand people, so it may not be worth her time and effort to learn it. English is very widely spoken in Zermatt, according to a travel site that I just checked.

Here's the 2017 clip. Check out Frida's ABBAchronistic mistake at 1 minute 30 secs

Yes, I'm German myself (not Swiss, though). And yeah, Frida has a very strong foreign accent when saying these two words. I cannot make out what she's saying during the bit you were referring to. Thomas doesn't have an awkward German accent, he sounds pretty normal for a Swiss person who speak quite a different version of German. People from the German part of Switzerland are fluent in both standard German and the Swiss dialect, though.

They didn't have a common language. German-born Hansi Schwarz, Björn's fellow Hootenanny Singers member, served as an interpreter.

Seeing as Frida spent a lot of time in Norway as a child, coming from a large family of people who most likely couldnt speak Swedish, and being raised by her grandmother, who its said couldnt speak Swedish when they first moved there, Frida most likely can speak Norwegian. She obviously prefers using Swedish tho!

I've also seen an article on a Reddit forum claim that Frida's mother was actually a Norwegian Sámi, and the Lyngstads were from a region with a big Sámi population, so maybe there's a possibilty she has a small understanding of a Sámi language? I have no idea how true that claim is though!