1) You can't use two-weapon fighting with ranged weapons. The rules for two-weapon fighting are for melee weapons only (PHB 195).
2) You can, however, throw two weapons with two-weapon fighting. Since thrown weapons still count as melee weapons (PHB 195). Note that the weapon in question seems to require both the light and thrown properties, limiting your choices to daggers, handaxes, and light hammers.
3) The Crossbow Expert feat lets you fire two loaded hand crossbows, but only for one round. You can use your Attack action to fire the first hand crossbow (since it is a one-handed weapon) and your bonus action to fire the other hand crossbow (since it is specifically a loaded hand crossbow as required by the feat).
4) However, you can't fire two hand crossbows round after round. Since hand crossbows have the ammunition property, you need a free hand to reload your hand crossbows, which you can't do while holding two weapons. If you fire two hand crossbows, on the next round you need to use your free object interaction to stow one hand crossbow, freeing up a hand to load and fire the other hand crossbow (PHB 146).
5) And yet, if you want to fire the same hand crossbow multiple times the Crossbow Expert feat basically gives you a bonus attack per turn. According to the Sage Advice ruling, at least--which honestly doesn't seem to support a rules-as-intended reading (SA).
6) You can only draw or stow one weapon on your turn (PHB 190). If you have the Duel Wielder feat you can draw or stow two weapons on your turn (PHB 165).
7) If you gain the Extra Attack feature, you can't use it with crossbows (unless you also have the Crossbow Expert feat) or black powder firearms due to the loading property of those weapons (PHB 147). You can fire multiple arrows from a longbow in a round as bows do not have the loading property, but cannot fire multiple bolts from a crossbow during a round--unless you have the aforementioned feat.
8) Firing at enemies in melee range gives you disadvantage on the attack (PHB 195). This applies to ranged attack spells as well. However, the Crossbow Expert feat negates disadvantage on attacking in melee range. The feat also negates disadvantage for spell attacks, oddly enough.
9) Firing at enemies engaged in melee or with friends whose bodies give it cover means that the enemy gets +2 to its Armor Class (PHB 196). The Sharpshooter feat negates that bonus for weapon attacks, the Spell Sniper feat negates it for ranged spell attacks.
10) As near as I can tell, there is no way to hit a friend when firing into a melee.
11) You don't get your proficiency bonus when attacking with alchemist's fire, holy water, or oil. Both are treated as improvised weapons used to make a ranged attack, so you get your Dex modifier to the d20 attack roll, but do not get your proficiency bonus added to the roll (PHB 147, 148, 151, 152). However, the Tavern Brawler feat gives you proficiency with improvised weapons, which would mean you can throw the above items at full proficiency (PHB 170). Although it isn't spelled out in explicit terms, it looks like you also don't get your proficiency bonus when attacking with a torch as a melee weapon.
12) The Archery fighting style does not give you a bonus to ranged attacks with thrown weapons. Since thrown weapons are still melee weapons, the bonus from the Archery fighting style doesn't apply to them (PHB 72).
13) You can't choose to knock a foe unconscious instead of killing them when you drop their hit points to zero with a ranged weapon. Only a melee attack can be used to knock a foe unconscious (PHB 198). Thus, you cannot knock an opponent out with a thrown rock or a sling stone. And you definitely can't use a ranged spell attack to knock someone unconscious.