How many times does a Mature Animal Companion attack per encounter without orders?

The Mature Animal Companion feat for Rangers (CRB p173) is really ambigious:

If you have the Hunt Prey action, your animal companion assaults the prey even without your orders. During an encounter, even if you don’t use the Command an Animal action, your animal companion can still use 1 action that round on your turn to Stride toward or Strike your prey.
(emphasis mine)

It makes a lot more sense with use instead of have, otherwise I might not even have a Prey for it to Strike.
But in that case, next round, when the Prey is still alive, will my Animal Companion just stand around?

Animal companion: roll additional HDs or not?

When a druid reaches level 3, his animal companion earns two hit dice. Do I have to roll them to give him more hp or is it only a number to use, for example, for spell effects? The manual also says that they “gain a Constitution modifier”, so I would roll them, but a level 3 animal companion might have more hp than the druid itself, which seems a bit overpowered to me.

At third-level, are rangers allowed to select a drake as their animal companion?

I wasn’t able to find anything about this in 5th Edition. A drake seems that it would exceed the 1/4 challenge rating stated in the PHB.

In this specific campaign, our Dungeon Master allows anything that is accessible on D&D Beyond not including Homebrew content.

I did find the Drake Warden Ranger archetype, which I assume is for Pathfinder, and thought it might be possible that I’d overlooked a similar variant in D&D 5E.

Is it possible to fool an animal companion?

Is it possible to fool an animal companion impersonating its owner? For example, if a druid is fighting with his party and its animal companion – let’s say a wolf – would its opponent be able to get the wolf attack an ally of the druid imitating the druid’s voice?

If it is possible, how can it be done? Is a skill check on Handle animal or Bluff a good way?

Would Vicissitude alone be enough to produce flying animal ghouls?

I’m running a Dark Ages campaign and one of the players is a young Tzimisce vampire, left in service of Gutka in Poland. While there, he decided to invent winged hussars several hundred years early, but instead of winging the hussar, he’d prefer to use Vicissitude III to shape horses into wing-bearing, flight-capable death cavalry machines, ghouled to their rider. Extra armour in bone included.

To me, this seems incredibly cool, yet I cannot see whether such proficiency in Vicissitude actually allows such a feat.

Is it viable for a Druid to have both Wild Shape and Animal Companion?

As a Druid, you can take both the Wild Order (gaining Wild Shape) and the Animal Order (gaining an Animal Companion) via Order Explorer (Druid Feat 2). To be most effective, you would likely wish to change into a battle form and fight alongside your companion. However…

According to the Animal Companion rules:

Your animal companion has the minion trait, and it gains 2 actions during your turn if you use the Command an Animal action to command it

From Command an Animal, the action has the Auditory Trait:

Auditory actions and effects rely on sound. An action with the auditory trait can be successfully performed only if the creature using the action can speak or otherwise produce the required sounds.

And according to the Polymorph trait (which is on all Wild Shape spells):

Unless otherwise noted, the battle form prevents you from casting spells, speaking, and using most manipulate actions that require hands.

From this, it appears that if you change into an animal form, you can’t effectively command your animal companion. However, Auditory doesn’t specify that you have to speak, only “produce the required sounds”.

So, can you consider your animal trained to take commands in various grunts and growls from your animal forms, or are you forever gimped into only using one or the other feature (barring special forms like Thousand Faces which isn’t considered a battle form, and thus not subject to the restrictions)?

How is animal anatomy accounted for in Pathfinder?

In the answer https://rpg.stackexchange.com/a/156870/3263 it is quite seriously suggested that (skeletal) horses should use trekking poles to increase their speed.

As far as I understand, trekking poles are held in hands. Horses would have a hard time grasping them and taking advantange of them due to reasons of anatomy.

For similar reasons, we might want to say that elephants have difficulty climbing, even though they have high strength. We might want to say that snakes have problems using lockpicks.

There is, of course, also the question is a horse would need some training to use those trekking poles, or would even agree to it. But let us focus on anatomy for now.

So, do the Pathfinder rules have any provisions taking into account such anatomical features of animals and monsters, or do they explicitly leave this up to the game master, or are they completely silent?

Does a Beastmaster Ranger’s animal companion gain more actions when its master becomes incapacitated?

This question comes from discussion in the comments to the question “Can my baboon animal companion use her wand of magic missiles?”

The beast master’s animal companion states:

[…] The beast obeys your commands as best as it can. It takes its turn on your initiative. On your turn, you can verbally command the beast where to move (no action required by you). You can use your action to verbally command it to take the Attack, Dash, Disengage, or Help action. If you don’t issue a command, the beast takes the Dodge action. […]

I’m unsure whether this is a list of the only actions that an animal companion can take during combat (and thus excluding options such as Use and Object and Hide).

Notice that this is different from what find familiar states:

[..] Your familiar acts independently of you, but it always obeys your commands. In combat, it rolls its own initiative and acts on its own turn. A familiar can’t attack, but it can take other actions as normal […]

The description of the Ranger’s Companion goes on to state:

If you are incapacitated or absent, your beast companion acts on its own, focusing on protecting you and itself. […]

Here there are no such action restrictions put on the beast companion. Does this mean that while you are Incapacitated your animal companion could now take actions such as Use an Object if they protected you, whereas otherwise it could not?