There are several nuances to the question of stability. First, there are different forms of stability that are entirely independent of one another. For example, mean-level (normative) changes (or lack of them) describe how people change in their traits on average (or don't). Then there is rank-order stability, which quantifies how stable are the differences between people (or their rankings in the traits); is the most extraverted kid in the primary school still the most extraverted of them in their school reunion 20 years later? The rankings of people can be (but actually are not) absolutely stable, whereas everyone can go up or down in the traits over time, if there is normative change. Differences between people can also become more accentuated over time (fan out), which does not require any normative changes or even changes in the differences between people: for example, more extraverted kids can become even more extraverted with time, and the other way around. Second, stability is not an all or nothing question and the reality is in the middle of the two extremes -- people are not fixed in their personality traits, nor all over the place. For example, differences between people tend to be quite stable over short (say less than a few years) to medium intervals (say 5 to 15 years), but as more and more time passes they increasingly swap their positions in relation to one another in personality trait scores. Mean-level changes, too, tend to be modest when we compare close ages but become stronger as the ages that we compare are more apart -- shifts are slow but persistent, and really continue into older age. When we look at age differences in many traits in combinations, then we can predict someone's age pretty accurately from their personality trait profiles.

On average and only describing the broadest patterns, people tend to become somewhat emotionally more stable (a bit less prone to being sad, impulsive, irritable), conscientious (a bit more organised, diligent, planful) and agreeable (a bit more trustful, cooperative, empathetic). They also tend to seek less excitement and social interactions, fantasise less and become more traditions-oriented. But it is important to realise that these shifts are quite small and only describe an "average person", which of course no one exactly is. So, any one individual can change in a different way. In most general terms, people tend to become more set in their ways as they age -- most of us develop our own characteristic profile of traits that sets us apart from others and stick with them. These changes can occur at any point in life, but most of them tend to happen in adolescence and early adulthood.

Neuroticism is a broad domain of more specific traits and, as a whole, it tends to decrease a little with age, on average across the population. But truth be told, the normative shift is quite small, so it only applies to a fraction of the population and may often be quite unnoticeable to the "naked eye". On the other hand, there are more specific traits within the broad Neuroticism domain that tend to decrease a little more with age, on average. For example, impulsivity -- finding it hard to control emotions or urges -- trends downwards with age a little more than many other traits linked with the Neuroticism domain.

On average, narcissism tends to decline with age. But this trend is quite small in magnitude, so it only applies to a fraction of the population and may often be quite unnoticeable to the "naked eye".

Yes, on average people report it somewhat easier to resist temptations as they age. In fact, this trend is also noticeable to those who observe others aging; that is, it is also visible when age differences are measured with personality trait ratings that people give about others that they know well rather than about themselves. But the average changes are quite small in magnitude, so they only applies to a fraction of the population and may often be quite unnoticeable to the "naked eye".

Emotional stability is defined as the opposite of Neuroticism, so another reply applies here, too. Neuroticism is a broad domain of more specific traits and, as a whole, it tends to decrease a little with age, on average across the population. But truth be told, the normative shift is quite small, so it only applies to a fraction of the population and may often be quite unnoticeable to the "naked eye". On the other hand, there are more specific traits within the broad Neuroticism domain that tend to decrease a little more with age, on average. For example, impulsivity -- finding it hard to control emotions or urges -- trends downwards with age a little more than many other traits linked with the Neuroticism domain.

When it comes to personality maturation, we may think about two things. First, there is a small normative trend for maturation in that the average trait levels in the population shift towards levels that are socially more desirable (the shifts are slow and not large, though). There are two main theories to explain this and I think the jury is still out there as to which one is more correct, or whether both are equally correct at the same time. According to one theory, the maturation pattern is hardwired into us through evolution. According to the other, this occurs because people take on new social roles that come with expectations for greater maturity and tend to comply with these expectations; if most people go through these role transitions at roughly similar periods in their lives, this leads to average trait levels shifting in the population. If you ask me personally, I would put my money on the the combination of the internally- and externally-driven pulls for greater maturation. Second, we can think of maturation at the level of individuals in that they may, on average, become increasingly well embedded in their unique circumstances -- or negotiate their place in life, so to say. Again, this may be because people tend to find suitable niches for themselves (for example, life circumstances and behavioural patterns that fit these) without necessarily changing their personality traits or because they change their personality to better fit into their environment, or both. If you ask me, I would again put my money on the the combination: people find niches that suit their traits and these niches reinforce the traits even further.