Aryea, of COURSE you can mix beef and chicken/turkey, veal, whatever, together. No kashrus problem, and many kosher stores sell bee/turkey chopped meat, and it is less fatty, less cholesterol, and lower in calories than traditional chopped meat, with no loss of taste.
As to liver and meat – kashered meat is kashered meat. Did you know you could technically kasher beef the same way you kasher the liver? The only reason we kasher liver as we do, is that it cannot be completely kashered through regular kashering means (i.e. soaking and salting). The blood will not completely come out unless it is broiled. Instead of asking your butcher (unless he is a rov), ask you LOR for his informed input.