Fiddlerman said
What dampens the sound the most is to reduce vibrations on the bridge and or top of the violin. Obviously the bills dampen vibrations a bit but try pushing them tight up against the bridge. You've probably heard of putting a clothespin on the bridge as well right?  

Yes, I've read about using a clothespin and it seems like a nice way, according to what I read. However I don't have a clothespin yet and don't know where to get it yet (there's language barrier for finding it too) so it's not an option yet.

Using so many bills work surprisingly well however, so this is the one I'm going to use unless it's harmful on the strings.

I didn't know that it's the bridge I mostly have to reduce vibrations on, so it's a useful information.

However, I still need to know whether the bills I'm using right now are harmful at all (or to what extent) on the strings, as I need to choose between not using them (not much of a choice), putting them on only when playing (if it's a bit harmful on the strings over time), or having them on all the time (if it's not harmful at all)

Fiddlerman said

I don't believe they are harmful. Especially if you don't slide them in and out...

Try taking soft paper (paper towel, toilet paper, foam) or a cotton clothe and stuffing it in that area behind the bridge to see if that dampens the instrument enough for you.   

I see, thank you!