"Betyr -det- at..."
The year 2000 belongs to the 20th century, in fact the last year of the 20th. (Like the year 0.)
So; because year 1 AD is the year they started counting (seems sort of logical to skip 0 once they decided to relate it all to the birth of God's son), it is the 1st century. 2001 is the 21st century/the 2000s. 2000 is the 20th century/the 1900s.
(And now I have to google have they talk about the centuries before year 0 :-) )
That is a good distinction:) And also you as a person can have meaning/influence in someone else's life, which sorts under "idea", since "you" become an object.
Hva betyr du for henne? what do you mean to her (what does she feel about you/what is your significance in her life), as in "you meant a lot to her", du betød mye for henne.
If I understand you correctly now, "do you mean that" would more often become mener du at. While betyr det at... is something like "does that mean that". Å mene is giving an opinion, often in terms of "what do you think about that". Å bety = having a meaning (not an opinion! A religion can have a meaning, but it can't have an opinion, that is the kind of difference I'm talking about for bety vs mene), so you can't say "betyr du at", it has to be an it/that (det/dette)