does 'ważne' also mean serious?
"serious" is "poważne" (and its forms).
What is the function of 'dla' in this sentence?
It's kinda like English "for".
Why is it wrong to translate this as' to me it is important' which is good english
Well, one could argue that we could also rephrase the original sentence to "Dla mnie jest to ważne", but ok, added.
Is "ważne" in accusative because of the "to", as in "to jest" ... ?
It's not Accusative. It's just an adjective on its own, it stays in Nominative.
It's neuter because of the neuter construction "To jest" = "This is".
Could the word order be changed to the English equivalent and still make sense? Like "To wazne dla mnie".
With stressing that it's important "to me, and not to someone else", yeah.
So how do you translate 'This matters to me' (which is what I thought the sentence meant)?
You could go with "To ma dla mnie znaczenie", but generally I guess that "This matters to me" could be a translation here, added.
And I wrote "It is to me important." Which way depends on what the speaker/writer wants to emphasize. And I did not know from the polish which, so I decided on my own to make important, important.
May be "for me"? Not "to me"?
I like this sentence! = a good reason for learning Polish.