Implied vol is (very loosely speaking) the risk neutral expectation of the realized volatility over the life of the option.
A 10Y implied vol is an average over 10 years, and therefore is relatively immune to short term spikes. It is slowly varying, relative to a 1M vol which only captures spikes in short term sentiment.
When the Vix (which is short term) went to over 150% in the crisis of 2008-9, you would not expect it to last for many months. Therefore the longer term vols did not spike in that extent.
It is essentially the same logic that applies to yield curves, where the 30Y rate moves in a much less volatile than the 1Y rate. The former reflects long term fundamentals, while the latter assesses the next business cycle and central bank responses.
Re (2) in your edit:
Implied vol skews are much more pronounced for short term options (when you have moneyness on the x-axis). After all, a 10% move is big over a day or a week, but not a big deal over two years. Also, just due to the law of large numbers distributions become more Gaussian in the long run, and the smile flattens out somewhat.
Every stock/vol surface will have some degree of 'stickiness' associated with it: Say, for example, that the spot is 100, and (strike, vol) pairs look like that (90, 40%), (100 ATM, 30%), (110, 25%). If now the spot moves down to 95, there are three effects in play:
Sticky moneyness: The ATM spot level is now 95, and the whole skew will have the tendency to be carried with the declining spot to the left, in order for the ATM option to keep vol of 30%. When you use time series of ATM implied vols, this is what you implicitly assume. The option with strike 90 will see its implied vol going down to 35%, and so on.
Sticky strike: The skew stays where it is in terms of strikes. Since options are contractually defined in terms of strikes, the implied vols of individual options do not change (even though you now observe the ATM vol to go up, from 30% to 35%).
In reality every stock, index or FX will exhibit a mix of moneyness and strike strickiness. As a rule of thumb, I would say the sticky strike dominates over short term moves for equities.
The above move (or not move) the skew left and right. But you also have:
- Spot/vol correlation: Realised vol is correlated with spot. This does not refer to any particular option, and will move the whole skew up or down. It just says that if the spot drops by 5% the world is more volatile by 2% (and the time value of all options increases, so to speak).
As long term skews are much flatter, spot/vol correlation becomes more important over stickiness.
This is my toy understanding and decomposition: spot/vol correlation (up/down) and stickiness (left/right). It is not uncommon for people to confuse left/right for up/down and conclude that there more negative spot/vol correlation than there really is. Especially when they use short term vols like the Vix.