What do you think of when you think of someone dual-wielding handaxes, or scimitars, or any other light weapons?  Speed.  Motion.  An unending barrage of blows. 

• Whenever you use a bonus action to make a melee attack with a weapon that you are holding in one hand, you can make one additional attack as part of that bonus action. 

Okay, that's basically Extra Attack for dual-wielders.  Prerequisite: 5th level. 

• When you make an opportunity attack while engaged in two-weapon fighting, you can attack with your other weapon as part of the opportunity attack. 

And there's a near-ribbon to round it out. 

I carefully phrased both of those to work with the Dual Wielder feat and anything else that lets you dual-wield non-light weapons, and the first one to work with any monk subclass that can attack with weapons with Martial Arts/Flurry of Blows. 

Clever. It allows spmeone willing to sacrifice 2 asi the ability to attack up to four times (or more if a fighter) while the level 5 restriction keeps a varient human from grabbing it and starting off with three attacks.

As for the flail, multiple rolls can slow the game if you end up on a roll. Instead, what if you just subtract 1 from the initial roll for each enemy until it no longer hits?

The issue with one roll is what happen if you have say 5 eneines with arround you and three have 1 ax and the other 2 have differebt acs

I want to weigh in here and say weapon feats are waste of effort. They come from a genuine RP flavour and fun place but ultimately the require explaining and review at the table, i.e. the wizard asks... what is that rule... can i do that ...etc. This is fine for one or two feats but for many weapon groups it becomes very unwieldy.

I think a major factor in these feats' appeal is that the weapon table itself is flawed. An example being a great and terrible tribal warrior with a spear does 1d6 damage, but does 1d8 with a rapier.... in this example I would say add a "martial" spear to the martial weapon table and adjust the damage rather than design a bandaid feat that players and NPCs have to take in place of something to compensate for a flawed weapon table

Just sayin'

Another thing that is missing, potentially by design, from the book weapon feats are ones for Versatile and/or Finesse weapons. There is a feat for Great Weapons and a Feat for Ranged Weapons that allow for a much more damaging use of them (sacrificing accuracy). I would think there would be something for Finesse weapons and Versatile weapons. I can see how those get complicated as they could stack with dual wielding or rogue sneak attack to get some crazy effects though. So there is that to consider. But "take some levels of rogue" if you want to be better with finesse weapons. Just irritates me that the only dex based fighters are either ranged, rogue or use a rapier for example...
I thought of something like:
Finesse Weapon Master (Fighting style)
   - Any melee weapon that you are wielding in one hand is considered to have the finesse property

Maybe turn that into a feat with some other effect. I wouldn't add to the dmg but maybe something for making you more likely to hit? like "When wielding a finesse weapon, you may choose to forgo part or all of your ability bonus to damage and add double that amount to your hit bonus for that attack? Or maybe just an equal amount? So you have the ability to be very precise (but less damaging than a 'brute'). Kind of the opposite of the -5 to hit +10 to damage. I don't like just flipping to just say you can get a +10 to hit by taking a -5 to damage. That feels like it lacks the "precision" this should have and it isn't a lot of math or extra rolls.

As for Versatile weapons, it really is about the fact that you really can't dual wield a versatile weapon like you could in old editions. The wording just doesn't work out for other feats and such (because a lot say "when wielding in one hand"). So there is a lot of torturous logic trying to get full 2 handed damage out of the weapon for all the attacks. Or silly work around. Again, I think the balance issues have to do with abuse you could put into dual wielding and getting unintended levels of damage output. Was thinking something like During your turn, instead of wielding your weapon in both hands, you may choose to be considered as dual wielding the weapon one handed in each hand. This counts as 'dual wielding" a different weapon in each hand for the purposes of applying any other feats or effects. You may make a bonus off-hand attack. Fighter fighting style is needed for off hand bonus damage and duelist wouldn't (for example). The Dual Weapon feat would give you the bonus AC etc.

Behold! The awesome power of Necromancy!!

I have created a Feat for use with whips. Rogues will find it particularly worth taking.

Whip Specialist:

Your expertise with whips allows you to make use of their full range and utility. In addition, you may use your bonus action to trip, disarm, or attack an additional time. 

• When you take this feat, you gain proficiency with whips.
• When you take the Attack action and attack with a whip, you can use your bonus action to make an additional attack with your whip, OR, as a bonus action on your turn, you may attempt to disarm or trip an opponent within your reach. The opponent must make a Strength saving throw. The DC for this is 8 + Attacking stat + proficiency bonus. If they fail, you may choose to trip or disarm them.
• Your range with whips is increased by 5'. In addition, you can use a whip to grasp an unattended Small or Tiny object within your whip’s reach and pull that object into your square. To do so, you must hit AC 10 with a melee attack. You can also use the whip to grasp onto an object within your whip’s reach as if it were a grappling hook, allowing you to swing on it like a rope. You cannot use the whip to attack while the whip is grasping an object, but as a free action, you can release the object your whip is grasping.