I think that's viable with BBs, with a few considerations:
-For legs it's quickly gonna get difficult to rely just on DBs. If you intend to work legs well in future as you get stronger, it's probably necessary to get a BB for something like squats. Then of course you'd also need a rack, so you'd have to consider whether it's worth it, or instead stick wth DBs for legs and not getting as much upside for something like legs. Just using DBs for legs you could definitely make some progress but would be limited. Besides squats, you could also do DB step-ups or jump up with them-plyometrics using weight, which magnifies the intensity while using less weight that you'd use in regular exercise.
-I'd add lying triceps extensions to your list, after biceps curls. Lower the DBs behind and below your head.
-Also i'd put shoulder press after the barbell rows-keep chest and back together, then do the militaries.
-Put deads last.
-Add cleans second to last.
-As far as using a split, i'd say follow your plan for a couple of months at least, then if you want to try a split, do half the weights day 1, the other half day 2, rest day 3 and repeat. Then compare with the original 3 day routine you started with and see which works better and which you prefer. Or alternate the use of both approaches from time to time if you like both.
-Cardio i definitely agree with 5-6 times a week if you're serious about weight loss and flab reduction. Don't worry about it affecting muscle gain, assuming you're eating good quality food often enough each day.