Tomek, welcome to the forum. Yes, you can re-paraffin the cheese. Don't try to just add paraffin to the existing (that doesn't seem to work well); instead, take off all the paraffin and completely re-coat it.
If you cut a slice out, you will probably want to go ahead and cut it in half -- I doubt that you would be able to get it sealed as well if there is a large concave in the shape.
Sure, you can paraffin cheese from the store, assuming you are talking about a paraffin-suitable cheese. (For example, I woudn't suggest using paraffin on a brie!) Are you wanting to do this in order to prevent mold, or to try to let it age more? I don't know how well the latter might work; I guess it would depend on how the store-bought cheese was made.
