Does a monk’s Unarmored Movement speed increase apply to the fly speed gained from a Fly spell?

A monk’s Unarmored Movement class feature increases the monks speed by 10 feet at level 2, and further at higher levels. According to this Sage Advice, this stacks with an Aarakocra monk’s fly speed, because that fly speed is innate to the race.

However, how does this interact with fly speeds gained from other sources, such as the Fly spell? That spell specifically states that “the target gains a flying speed of 60 feet for the duration.” Can this gained flying speed then be improved by a monk’s Unarmored Movement, giving a level 2 monk a flying speed of 70 feet with the Fly spell cast on them?

Does rogue’s vest bonus damage apply separately for each precision damage source?

Rogue’s vest (MiC 130) grants users with "the skirmish, sneak attack, or sudden strike ability" an extra 1d6 damage "when making such an attack"

Does this mean that, for example, a scout 1/rogue 1/ninja 1 that moves 10 feet and attacks a flat-footed opponent (who lacks uncanny dodge) deals 1d6 base skirmish damage plus 1d6 extra damage because they made "such an attack", as well as 1d6 base sneak attack damage plus 1d6 extra damage for making "such an attack" and 1d6 base sudden strike damage plus 1d6 extra…For a total of 6d6 precision damage? Or is the "attack" only granted the item’s bonus damage once, for a total of 4d6 precision damage?

Does the Hexblade Warlock’s Hex Warrior feature apply to a magic weapon that is transformed into your Pact Weapon?

The Hexblade Warlock’s Hex Warrior feature states (emphasis mine):

[…] If you later gain the Pact of the Blade feature, this benefit extends to every pact weapon you conjure with that feature, no matter the weapon’s type.

Meanwhile, the Pact of the Blade Warlock feature states:

[…] You can transform one magic weapon into your pact weapon by performing a special ritual while you hold the weapon. You perform the ritual over the course of 1 hour, which can be done during a short rest. You can then dismiss the weapon, shunting it into an extradimensional space, and it appears whenever you create your pact weapon thereafter. […]

Does a magic weapon that you have transformed into your pact weapon benefit from Hex Warrior?
Does it count as a weapon you have conjured using Pact of the Blade?
Does the answer change if you shunt the weapon away and then make it appear afterwards?

Does Sword of Sharpness’s maximize damage rule apply to a Rogue’s Sneak Attack damage? [duplicate]

If a rogue hits someone with a scimitar of sharpness and the preconditions for sneak attack are in place, does the rogue also get to maximize the damage of sneak attacks?

For reference the Sword of Sharpness states:

When you attack an object with this magic sword and hit, maximize your weapon damage dice against the target. […]

Does the Shepherd Druid’s Mighty Summoner feature apply to creatures summoned through their Faithful Summons feature?

Mighty Summoner says (emphasis mine):

Any beast or fey summoned or created by a spell that you cast gains the following benefits: […]

Faithful Summons says (emphasis mine):

If you are reduced to 0 hit points or are incapacitated against your will, you can immediately gain the benefits of conjure animals as if it were cast using a 9th-level spell slot.

Does the phrase "as if it were cast using a 9th-level spell slot" indicate that we should treat this as if we are casting the spell, thereby allowing us to apply Mighty Summoner to the creatures summoned?

Note, this question is different from this Q&A, as it is unclear if Faithful Summons counts as casting a spell: Would the 6th level Shepherd Druid’s Mighty Summoner feature works on summoned creatures not made from spells

Can you apply Hex damage when the target is immune to the initial damage?

The Warlock is fighting a Ochre Jelly. On his turn, he cast Hex on the Jelly as a bonus action, then hits it with his Short sword. The Ochre Jelly is immune to the slashing damage, so the attack does zero damage regardless of what the Warlock rolls, however is the Hex able to proc, and deal 1d6 necrotic damage to the jelly?

Hex states (PHB p.251):

You place a curse on a creature that you can see within range. Until the spell ends, you deal an extra 1d6 necrotic damage to the target whenever you hit it with an attack. […]

So although the attack hit, would the Jelly still take the Hex’s additional damage when it is immune to the original damage of the attack?

Does Natural Explorer’s double proficiency apply to perception checks while keeping watch?

The Natural Explorer class feature is sort of vague about what skill checks count

When you make an Intelligence or Wisdom check related to your favored terrain, your proficiency bonus is doubled if you are using a skill that you’re proficient in.

I emphasized related to, because it doesn’t say "while in," so I’m wondering whether keeping watch in your favored terrain counts as related to your favored terrain. This could represent something like being more familiar with what’s naturally around, and so you have an easier time spotting what shouldn’t be — i.e. the approaching enemy.

Does it apply?

Would Precision Attack apply for a melee spell attack?

I’ve searched here and in various reference books but can’t find this specific answer. The description of the Battlemaster Precision Attack maneuver states it can be used for any weapon attack. Thorn Whip for example uses magic to create a weapon….that is not magic. So would that "weapon" attack count towards as being able to used with Precision Attack even though the attack is using a spell?