These da- particles (and hier- particles, too) have a demonstrative function. You are pointing fingers here. If you feel you don't need to point to something, you can always leave them out. (Hint: da translates there, hier translates here, which is the pointing finger.)
This is the case for all your examples. They are correct with or without the particles. The meaning is also the same because you explain the thing in question in the following clause.
But when you aren't explaining the thing in question, things get complicated.
Er hat etwas davon genommen.
He has taken something of it.
Er hat etwas genommen.
He has taken something.
Both sentences are grammatically right. But the second has no finger pointing to the thing in question. So you can't leave davon out here without changing the meaning. Same for all other da- particles.
And finally there are sentences in which such a da- particle cannot be left out because it drops into the function of an object:
Davon habe ich noch nie gehört.
I've never heard of it.
Damit geht es los.
This is where it starts.
One could rearrange the German sentences ("Ich habe noch nie gehört" and "Es geht los") but both the meaning and the structure are changing so let's assume these are completly different sentences.
