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.
USDA Zone 7A Elevation 1400 ft