Borrowing from @Codestrife's answer here
The rustling leaves usually indicate that there are pokemon near that area. Going and walking around near that area gives you a higher chance to encounter Pokémon.
Keep an eye out for rustling leaves, hinting at where critters may be
lurking and simply hang out in a suspected region for the increased
chance of an encounter. - Source
Therefore, the reason you don't always see Pokémon in rustling grass is because there is only a higher chance to encounter them there and not a guaranteed chance of encountering them. You just have bad luck when you don't encounter them.
Not really, no. The only Pokemon that would be considered to be 'only hatched from an egg' are the region-restricted Pokemon. But, even then, if you were to travel to one of those countries, you could of course catch those as well. The region-restricted Pokemon can be seen here: What are the regional Pokemon?
Edit: I feel it is important to add that this is still a pretty hotly debated fact. There was a survey done which claims to conclude that out of approximately 40,000 hatched eggs, none of the Pokemon were region-locked Pokemon. However, there are some people who claim (with evidence) that they have hatched region locked Pokemon. Some of these people even claim to have spoken to the person who created the aforementioned survey, only to have that person dismiss their claims as lies or 'hacking'.
So, right now, I am leaning towards that it IS possible to hatch region-locked Pokemon, however, there is yet to be 100% conclusive evidence either way. You can see some of the threads on Reddit where users have made claims for both sides.
Edit 2: Just to be clear, the answer to the actual question at hand here still appears to be no, the edit above is just some additional information, some of which may be a bit beyond the scope of this question.
Best Answer
Based on this Reddit post, this appears to be a bug when your scroll from incubated eggs to non-incubated eggs.
I have verified this by scrolling through my eggs and the number will stay blue when I scrolled through at least two incubated eggs.