The Ape is proficient with both of those skills. From the D&D5e SRD:
The Skills entry is reserved for monsters that are
proficient in one or more skills.
That same document has a Proficiency Bonus by Challenge Rating table that says that a CR 1/2 creature, like the Ape, has a proficiency bonus of +2. We can then take the stat bonuses from the 16 Str (+3) and 12 Wis (+1) to get the Ape's total modifiers to those skills.
So to determine what the Ape Companion's actual modifiers are for those skills you would take the stat bonus (+3 and +1) and add the ranger's proficiency bonus. You would do the same thing for the other skills you choose for it to learn.
Not quite as invisibility since it has its own caveats, emphasis mine.
You are also adept at evading creatures that rely on darkvision. Such
creatures gain no benefit when attempting to detect you in dark and dim conditions. Additionally, when the DM determines if you can hide
from a creature, that creature gains no benefit from its darkvision.
UA: The ranger, revised P. 8
The main difference is that, invisibility does not end when you are detected by other means that are not magical or with special senses but, in the ranger case, the condition/ability ends as soon as the ranger is detected.
The invisibility condition in PHB 191.
An invisible creature is impossible to see without the aid of magic
or a special sense. For the purpose of hiding, the creature is heavily
obscured. The creature’s location can be detected by any noise it
makes or any tracks it leaves.
Attack rolls against the creature have disadvantage, and the creature’s attack rolls have advantage.
Now, about detection; attacking or casting a spell make you lose the benefit as stated in PHB. 195. Also, there is a big difference between dark and dim conditions (PHB. 183). The main difference is that with normal sight you can see the ranger in dim conditions but you are blinded in dark conditions. Therefore, the ranger in dim condition is not treated as if it has invisibility/heavily obscured, the ranger is treated as if in dim condition.
(PHB 195) If you are hidden—both unseen and unheard—when you make an attack, you
give away your location when the attack hits or misses.
(PHB 183) A given area might be lightly or heavily obscured. In a lightly
obscured area, such as dim light, patchy fog, or moderate foliage,
creatures have disadvantage on Wisdom (Perception) checks that rely on
sight.
A heavily obscured area—such as darkness, opaque fog, or dense
foliage—blocks vision entirely. A creature in a heavily obscured area
effectively suffers from the blinded condition.
Thus, against the ranger when trying to detect him in dark or dim light condition, a Dark Elf and a Human are not treated differently, as if they have the same visual capacities.
As an example, by courtesy of Keithcurtis; Robbie the Ranger and Frank the Fighter are trying to sneak past Danny the Drow and Harry the Human in a dimly lit cavern. Harry has disadvantage on the opposing perception on both the sneakers, while Danny only has disadvantage against Robbie the Ranger.
Best Answer
Unearthed Arcarna are all unofficial rules and only usable by the agreement of the players at each particular table, particularly the DM.
In the case where an unofficial rule1 cites an official rule2 which is then superseded by another unofficial rule3 then if you are going to use the first unofficial rule1 then you need to consider as a table what the implications are of changing to the second unofficial rule3 and make your decision.
1 - Unearthed Arcana "Kits of Old", Fighter Archetype: Scout incorporates the Ranger class feature Natural Explorer.
2 - Ranger class feature as published in the PHB.
3 - Ranger class feature as published in Unearthed Arcana "Revised Ranger".