How do I count regeneration spells against the Druid’s daily and per-battle total?

The level progression chart for the Wild Healer Druid (13 True Ways, page 63) has both daily and per-battle uses for regeneration spells. Does this mean that a druid can cast the spell the per-battle amount in battle, and then expend daily uses whenever they please over the adventuring day? Or is the per-battle use a hard cap on usage per battle, leaving daily uses for use between combats?

For an example, I have two per-battle uses and one daily use of the spell on level 4. Can I use both of my per-battle uses and the daily use in a single combat encounter?

Count bridging edges in a family of two component forests

I am given a (simple, undirected, connected) graph $ G = (V, E)$ and a fixed spanning tree $ T$ in this graph. Removing an edge $ e\in E(T)$ from $ T$ splits it into a spanning forest $ F^e$ with two components $ F_1^e$ and $ F_2^e$ . I am interested in the number $ c(e)$ of edges in $ G$ that connect $ F^e$ i.e. with one vertex in $ F_1^e$ and the other in $ F_2^e$ .

I would like to compute the number $ c(e)$ for all $ e$ in $ T$ simultaneously. This can be done naively in $ O(|V||E|)$ . Is there a faster way to achieve this?

The graphs I am working with are small-world graphs. In particular the average distance between nodes in $ G$ can be assumed to be small.

Do enchantments count as magic when it comes to magic immunity?

I was looking at a construct’s immunities and noticed “immune to magic” in its list. Naturally, this means you can’t really cast spells at it. But what about weapon enchantments? Do enchancement bonuses have no effect when attacking these creatures? Do enchants like flaming and frost not do damage to it? Furthermore, would an alchemist’s bombs damage the creature at all? Since they explode using the alchemist’s own magical powers.

Do spells count as “Class Abilities” for the purposes of the “Sanctified Slayer” archetype?

The Sanctified Slayer Archetype says,

“At 1st level, a sanctified slayer gains the slayer’s studied target class feature. She uses her inquisitor level as her effective slayer level to determine the effects of studied target.”

The Slayer’s Studied Target feature says,

“A slayer can study an opponent he can see as a move action. … The DCs of slayer class abilities against that opponent increase by 1.”

Do spells count as a “class ability” for this purposes ? That is, would a Studied Slayer Inquisitor’s spell DCs get a +1 bonus when he uses Studied Target ?

Does using an Animated Shield count as ‘wielding a shield’ for Unarmored Defense?

Does using an Animated Shield count as ‘wielding a shield’ for Unarmored Defense? Specifically, would using it inhibit a monk’s unarmored defense?

And does the Animated Shield require proficiency with shields to use?

I would say that logically a floating independent shield does neither, and that the phrase “as if you were wielding it” says no, but I’d like a second opinion before I make any rookie assumptions about the nature of magic items.

Does Scorching Ray being fired at a single target count as one attack for the purpose of the Help Action?

Nin’Zar, the imp familiar, likes its cushy new assignment serving a Pact of the Chain Warlock. So, it wants to help its master as much as possible by using the Help Action when its master casts Scorching Ray.

The spell description for Scorching Ray says:

You create three rays of fire and hurl them at targets within range. You can hurl them at one target or several.

According to the Help Action,

You feint, distract the target, or in some other way team up to make your ally’s attack more effective. If your ally attacks the target before your next turn, the first attack roll is made with advantage.

When someone makes multiple attacks, they are separate, sequential events that happen during the course of that player’s turn. For instance, with Two-Weapon Fighting, a player makes an attack event then makes a Bonus Action attack event. When a fighter uses their Extra Attack feature, the multiple attacks are again separate, sequential attack events.

However, since the duration for Scorching Ray is ‘instantaneous’, if you fire all three rays at one target, it can be argued that this would count as one attack event. Just like firing both barrels from a shotgun at the same time would be one attack event. If this is the case, then the Help Action could give Advantage to each of the to hit rolls.

Does Scorching Ray being fired at a single target count as one attack for the purpose of the Help Action?

Can a ranged weapons ever count as melee weapons?

In Pathfinder, is it possible to use a ranged weapon with feats and abilities like Diva Strike which normally require a melee weapon, if the weapon is fired at melee range? It’s fairly easy (albeit feat intensive) to make a ranged weapon threaten (Snap Shot) and not provoke attacks of opportunity for firing (Point Blank Master) or reloading (Deft Shootist, or use a bow), but qualifying for other abilities seems more difficult. I’m not talking about thrown weapons here, but projectile ranged weapons (preferably firearms).

Solutions from reputable third party sources and 3.5 are also acceptable.