Are these verbs + adverb combos common - this is kind of like "pop up"? I suppose they are idiomatic...
Yes, you can compare it to pop up. They’re called particle verbs (partikelverb) in Swedish or phrasal verbs in English and they are very common. :)
In English: He shows up on the screen. or: He pops up on the screen.
In Swedish: He dives up on the screen.
Shouldn't the word "skärmen" (and all definite nouns) have a grave accent? It sounds really weird...
It has a grave accent (accent 2) in this example but it should have an acute accent (accent 1). But it is not true that all definite nouns receive the same accent. It depends on what accent it has in the indefinite form. This differs from the plural ending -ar, which always yields accent 2 (grave accent).
Tackar! I mistakenly said grave accent instead of acute accent. It's indeed not true for all definite nouns, but it IS true for all definite SINGULAR nouns, right?
No, I’m afraid not. It depends on what accent the noun has when it’s indefinite. For example and ’duck’ has accent 1 (as all words with 1 syllable) whereas ande ’spirit’ has accent 2 (which is common for nouns ending on the Swedish ending -e).
When you make these definite, they both become anden, but ’the duck’ has accent 1 and ’the spirit’ has accent 2 since that’s what they had in the indefinite form.
I can recommend watching this video made by our moderator Blehg: https://www.youtube.com/watch?v=lXp7_Sjgm34
Does the word skärmän (cutting men) also exist? If so, would it differ in pronunciation from skärmen?
That's what the voice says. The word doesn't really exist in the sense that it's not in dictionaries and I've never heard it, but we'd easily create it if we needed it.
For more detail, see the answers to NirnirLevy above.
So one guy seems to pronounce it similar to an f and the other pronunciation is similar to the one from duolingo.
the biggest difficulty for me is that it's not just some sort of throaty Dutch g (ch) but also that weird transition to ä ... like chä. Dunno ... it's weird.
I agree the two examples sounded different. Perhaps because they are from different areas with different accents. I liked the second playlist of pronunciations here (scroll down to rule#2): https://blogs.transparent.com/swedish/the-mysterious-swedish-sk/
Assuming they really were from different areas I would choose the f version of that pronunciation any day :D