As written, the ranger gains advantage on all initiative rolls and on (most) first-round attacks.
The relevant portion of the class feature Natural Explorer is simple:
- You have advantage on initiative rolls.
- On your first turn during combat, you have advantage on attack rolls against creatures that have not yet acted.
You have advantage on initiative rolls. Is it an initiative roll? Then you've got advantage.
You're attacking someone? Did they act yet? No? You've got advantage on that attack.
This clearly contradicts the intent of the class. Or does it...?
The opening line of Natural Explorer sets the tone:
You are a master of navigating the natural world, and you react with swift and decisive action when attacked.
It seems like you're reading onto that line the proviso "react with swift and decisive action when attacked in the natural world." But it's not there in the text. (To be fair, that's the read I gave it at first, too.)
Most of the features of the new ranger do tie into the nature theme. But this isn't the only that's just a pure buff to combat: Fleet of Foot, Vanish, and Feral Senses all would apply (as written) equally-well in an urban or dungeon environment as in overland.
The intro to that UA clearly states that the class--both as a whole and its features considered severally--was just seen as weak and unfun. It's your call as to whether they've gone too far pumping some power and fun into the Ranger, but that's exactly what the authors were trying to do.
Yes
Your companion uses your proficiency bonus rather than its own.
It is important to note that it says, without condition, that the companion uses the Ranger's proficiency bonus. This means that, from this point on, it's proficiency bonus is the Ranger's proficiency bonus. Think of it as erasing the value on the creature sheet, replacing it with the Ranger's value, and then recalculating everything from there.
Upon looking at the UA document again, this is further supported as such:
Keeping Track of Proficiency
When you gain your animal companion at 3rd level, its proficiency bonus matches yours at +2. As you gain levels and increase your proficiency bonus, remember that your companion’s proficiency bonus improves as well, and is applied to the following areas: Armor Class, skills, saving throws, attack bonus, and damage rolls.
While the wolf has a listed proficiency bonus of +2, nowhere is it stated that this bonus is already included in the damage of the wolf's attack. We may infer that this damage is from the wolf's DEX mod, as is supported by the fact that the base to hit is +4, which would be +2 from proficiency and +2 from DEX, matching expectations for standard application of proficiency bonuses. The wolf's damage should be increased by a flat 3 points, making the roll 2d4+5, the same as you have stated. Furthermore, applying +3 to the base 13 also matches your stated 16 AC, and replacing the +2 with proficiency with +3 also results in a +5 to hit when added to the DEX mod. It is not explicitly stated that the bite is a DEX-based attack, but this is the only value that makes sense from the creature stats. Your math looks right.
Bonus Answer: No, the damage dice of the wolf's bite attack do not scale. It is important to consider that the wolf companion is not intended to be as powerful as an extra PC, but is instead part of the power of the Ranger to whom it belongs. Applying proficiency bonus to a damage source is a benefit other classes do not have, and this comes from an attack that does not require the use of any of the Ranger's actions. Also, consider that this attack has the potential to knock a target prone, leaving it more vulnerable to melee attacks until it has the opportunity to stand. Such a tactical advantage is certainly not weak.
Best Answer
This article does an excellent job of describing in detail the changes between the stock ranger and the UA Ranger Revised, but I'll summarise for the Stack. Generally the Ranger is made more mobile, its abilities more widely applicable, and attack more dangerous, but probably the most important change is the introduction of the Beast Conclave archetype, as a direct redesign and improvement to the Beast Master archetype.
The base class changes include:
The Beast Conclave archetype works drastically differently to the original Beast Master archetype, which is great, because Beast Master Rangers are the single worst class in the core PHB. The improvements are many:
The other new archetype from the Ranger Revised, "Deep Stalker", made it out of UA into published status in Xanathar's Guide to Everything as the "Gloom Stalker", so I won't discuss it here.
Essentially, the Ranger Revised UA material presents a ranger with more general utility in all circumstances, abilities that support it being an amusher/skirmisher with enhanced mobility, more dangerous attacks and also the option to play the traditional ranger archetype with an animal companion that isn't an underpowered mess.