The Feats rule is in play.
There has been a massive amount of posting on the official forums about some of these (especially hand crossbows). I have summarised my thoughts and rulings below.
Only applies if your weapon is a melee weapon. I.e. not darts.
Only applies to melee weapons. Does, however, apply to throwing them.
No dual wielding hand crossbows.
First bullet point: This applies to any melee weapon, regardless of whether or not you are proficient. This includes improvised weapons. You can use this feat in a bar brawl!
You gain proficiency with shields, if not already proficient.
The abilities of this feat only apply if you are using the weapon two-handed.
First bullet point: The bonus attack uses the same ability modifier as the main attack. The ability modifier does add to the damage. This is not two-weapon fighting, so the Dual Wielder feat does not apply.
Only applies to ranged weapons.
If you want to be a dagger-throwing master then just use darts, and call them "throwing daggers".