[RPG] Can See Invisibility reveal an Unseen Servant

There are distance limitations on Perception checks in the rules, establishing that sight is not limited only by cover or lack of light. The limitation doesn't appear to be an abstraction of cover since the likelihood of nearby cover is also mentioned apart from the distance limit. Based on the reasoning given in the various terrains, it appears that distance limitation represents an abstract combination of terrain folds, vegetation, distortions in the air, and simply the inability for an observer to distinguish an object from the background on which it visually sits. (See the part about visibility in mountains being both a very short number and alternatively very far as determined by the DM's map of ridgelines, and the visibility in the desert being limited in part by heat shimmers in the air.) Furthermore, these limitations are mentioned in addition to limitations caused by obstructions to light of sight, making these limitations explicitly apply even when you have line of sight and the target is not in cover:

In plains terrain, the maximum distance at which a Perception check for detecting the nearby presence of others can succeed is 6d6 × 40 feet, although the specifics of your map might restrict line of sight. Cover and concealment are not uncommon, so a good place of refuge is often nearby, if not right at hand.

Unfortunately, in the set of terrains they failed to include an aerial "terrain" or even an above-water terrain, so there are no rules-as-written distance limitations for flying creatures outside of terrain like forest (where the canopy would restrict vision between creatures on foot and in the air). The limitation in plains terrain is 6d6×40 feet, but I don't think anyone could convincingly argue that this applies to flying creatures, given the rules-as-written distance limitations in mountains (as mentioned above).

However, the precedents in RAW strongly imply that there is a limitation based solely on the fact that air can obstruct vision optically, but the DM is on their own to figure out what it should be. There is no RAW answer. Personally I would either try to develop a table based on real-world principles of visibility, or I would build something more game-able like "1 mile per size category" or something to that effect.

If the invisible creature is stationary he gets a +40 to his stealth check.

If the invisible creature is moving he only gets +20 to his stealth check.

The act of rolling a perception check to detect a stealthy invisible creature is completely unrelated and unaffected when trying to sense using 'auditory senses only'. A standard perception check takes all senses into account. (If pathfinder was more simluationist then you might actually provide a penalty to the perception check when using 'auditory only' because they may miss some visual clues an invisible creature makes other than sound, such as footprints or a tree branch swaying)