The spell does exactly what it says it does, and no more
Choose one object weighing 1 to 5 pounds within range that isn't being worn or carried.
This means that you can't use it on an item that you are carrying, so you can't use this spell on the crossbow bolt hidden in your sleeve. You probably can't cast it on a crossbow bolt anyway, since it most likely weighs less than a pound. However, you can get around this limitation by casting it on nearby objects, like rocks, or by dropping the item you want to catapult first.
Additionally, you don't get any critical or sneak attack damage because this spell requires a saving throw, not an attack roll. This question explains why there are no critical hits on spells that require saving throws. Similarly, the Assassin's Assassinate feature only applies to attack rolls. Thus, you only get the 3d8 damage from the text of the spell.
Finally, it's reasonable for your DM to rule that sharp items could deal piercing damage, but that would be a houserule. Officially, every item flung by Catapult deals bludgeoning damage--if that's what your DM has decided, he is supported by the rules.
Whistling is probably not an appropriate somatic gesture
PHB 203 states,
Spellcasting gestures might include a forceful gesticulation or an intricate set of gestures. If a spell requires a somatic component, the caster must have free use of at least one hand to perform these gestures.
Which suggests that spells that require somatic component require hand motions. Whistling is arguably a verbal component, rather than somatic.
There is no rule. It's up to your DM.
Don't mistake the game's rules (or lack thereof) for laws of physics in the D&D universe.
There are a lot of areas where the rules don't get specific about every detail of how something works because it's not, generally speaking, important. This is one of those areas.
For the purpose of using alchemist's fire in a fight, it burns for some indefinite amount of time that exceeds the length of the fight. Even two minutes is usually much longer than any fight lasts, so 'until extinguished' is sufficient definition for that purpose.
Similarly, presumably the flame produces some amount of light, but how much isn't specified, so it's left up to the DM to decide. That doesn't mean it produces no light. It just means it's not specified.
Best Answer
This is up to the DM
The pedantic answer is that spells and effects only do what they say. This means catapult only deals damage to the flask, not activating its features. You have not taken the action nor made the ranged attack with it that it describes. How many hit points any one object has is also up to the DM, but using the suggested hit points from the DMG (p. 247) a resilient tiny object has 2d4 hit points, so it is reasonable to assume the flask is destroyed. However, the alchemist's fire has no description for what happens when it is destroyed, so it is on the DM.
Your DM might use the base description as a basis for what should happen, and apply the fire damage to the target. Or, they may rule that it does not hit in a sufficiently focused manner to apply harm to the target and so the target does not suffer damage. The main perceivable argument for not allowing this, is not setting a precedent for applying real-world logic to the game rules, which might benefit some characters and their abilities much more than others and/or eat up too much time at the table with arguments. On that note, as will any case of a strategy having ambiguity, ask your DM ahead of using it (possibly outside of game time) on how they would rule, so you know that before using it.