Re: sugar syrup
Syrup ratios are generally based on weight of the ingredients. Water is 8.3 lbs per gallon, but for convenience many round it off to 8 lbs / gallon. So your ratio is 25:16 which is very close to 5:3, which should be suitable for typical 2:1 purposes.
As far as floor sweepings sugar, unless you have reason to believe that it is contaminated with something more serious than dirt, it should be fine. I have used sugar that was improperly stored and suffered rodent damage, making it no longer suitable for humans. My bees didn't care and did fine with it.
. . . . . . "Reality trumps ideology." - - [Crofter - 2017]