You have asked several questions and I'll answer them to the best of my knowledge
I won't limit myself to the raid subject as you asked about fractals as well, however I need to make it clear that I've stopped playing them on a regular basis quite long ago. Thus not everything I say about fractals must be 100% accurate.
Whether tanking or not the main role of support Chronomancer in a raid squad is to provide their allies with 2 boons: Quickness and Alacrity, preferably with 100% uptime. Any rotation designed for those builds has this as a primary goal. Specific builds and rotations differ between each other because 1) this goal can be achieved by different means and 2) they achieve different secondary goals.
To complete primary goal most builds maximize Boon Duration (which affects both Quickness and Alacrity), in other words they get it to 100%. That can be done by using equipment and upgrade components with attribute combinations containing Concentration and consumables rising this attribute (when it comes to attribute combinations it's also important to pay attention to Toughness). There are also some upgrade components affecting directly Boon Duration - prominent example here is Superior Sigil of Concentration. Some builds will also utilize trait Chaotic Persistence.
To be useful in a raid squad you should prepare the proper gear and learn a rotation allowing you to keep high uptime of two primary boons at a reasonably high level. As for the rotation focus on skills which contribute to uptime of those boons to your allies (Signet of Inspiration, Tides of Time, Time Warp, Well of Recall, Well of Action) and skills allowing to use former skills more often (Continuum Split, Mimic).
What is also important to know is that in the current version of the game 100% uptime of Quickness is impossible to reach alone. However it isn't a problem as long as there are two support Chronomancers in a squad and both use trait Blurred Inscriptions. It allows them to help each other with enhanced Signet of Inspiration.
The situation in fractals is different. Most fights last shorter then in raids. Mesmer's wide palette of skills with high utility value comes more into play. As I mentioned currently there is also no way to reach 100% uptime on Quickness. Also it's easier to coordinate in 5-man party than in 10-man squad. Finally, fractal potions can be used to rise Concentration opening more gearing options. With factors like these, in my opinion, knowledge of encounters and instabilities, and how Mesmer's skills can be used in them is as important as putting an effort into keeping boons up.
I want to add that I write "support Chronomancer" because I'm fairly certain that's what you're asking about. While playing Chronomancer as a damage dealer (DPS) is possible it's a completely different story.
It's best if you have possibility to start tanking when you feel comfortable with an encounter. Even better if you feel comfortable with it as a non-tanking Chronomancer. That way you can focus during learning process on specific task of tanking and you shorten time required to get the hang of it. While for some people it's better to throw them in at the deep end, in a raid environment it's not the best solution as there are always 9 other people in squad whose time should be considered.
With that said I also must stress that tanking in Guild Wars 2 is much easier than in other MMOs. Here tank is only a "guide" which boss follows. When you play as a tank your responsibility is to make sure boss is at the correct place, in the correct time and facing in the correct direction - according to utilized tactic. In most other games on top of that, tank needs to use certain skills to ensure that boss is focused on that tank ("holding aggro/threat"). Only difficulty which tanks have here, but to lesser extent compared to other MMOs, is staying alive. For example tank often needs to deal with frontal attacks of the boss, while rest of the squad doesn't (this is partially mitigated by higher Toughness).
So when you are comfortable with a specific encounter, learn the tactic you want to utilize from tank's point of view (boss positioning, which attacks need to be avoided and how they can be avoided). With that you are good to start practicing.
Interesting question and I can answer it as I have lots of hours spent in open world playing support Chronomancer raid builds.
When you participate in Group Events you can do mostly what you would do in a raid. Your supportive capability is just as useful. One thing I'll stress is that you have easy access to a lot of CC skills.
When it comes to solo play, on the other hand, those builds can be quite curious to play. They aren't very fast in killing enemies. They aren't that great in mitigating taken damage (unless you play high Toughness build). However they have a variety of skills allowing to avoid enemy attacks, as well as many ways to easily interrupt them, So, in my opinion, it allows an interesting play style.
Like i mentioned above, certain skills are more important in rotation than others. But there are also three factors connected with this concern.
The first one is keeping boons on yourself. Most builds use a trait Improved Alacrity, which shortens duration of Alacrity on you. However you also have access to a lot of skills which give two primary boons only to yourself. Thus uptime on yourself isn't the best measure of how good you keep them on your allies.
The second factor follows from current version of the game. As I mentioned above Blurred Inscriptions make uptime in your sub-squad also dependent on the other support Chronomancer.
The last one is how much boons you spread manage to reach your allies. This is dependent solely on stacking - yours and your allies'. This factor impacts highly Tides and both Wells, Signet and Warp are affected less.
With all these reasons it's not as easy to track uptime on allies as it has been in some past versions of the game. While not the best solution, checking own boons is still somewhat helpful. Setting squad interface into mode which shows only own sub-squad similar to a party allows to track boons on them directly. You can also consider asking your co-raiders for feedback about this.
I already wrote quite a long post and support Chronomancer is a book-size topic. So the last thing I find worth touching (at least briefly) which supplements what I already wrote are "secondary goals," as I called them above.
Many rotations, even though they are designed for support Chronmancers, try to maximize damage output as a secondary goal. Because of the primary goal, this in all previous and current version of the game leads to builds which have damage significantly lower then builds optimized for dealing damage. The differences in numbers are large enough to say that maximizing Chronomancer damage makes difference only for hardcore raiding groups.
There are rotations which take advantage of synergy between traits Blurred Inscriptions and Inspiring Distortion. The ability to give 5 allies Aegis with skills Distortion and Signet of Inspiration (and Signet of the Ether if taken) opens room for tactics where squad doesn't try to normally avoid certain attacks, instead using Aegis against them. Those tactics require Chronomancers to adjust their rotation so that skills I just mentioned are aligned with such attacks.
Another group of rotations are those trying to maximize number of boons in the group. Since Chronomancers are able to share all boons with Signet of Inspiration if they are already present on them, those rotations make use of certain traits (especially Bountiful Disillusionment but also other Chaos traits) to provide them with a variety of boons. Aim of this is to make use of traits which have an effect scaling with number of boons (for example, Elementalist has a trait Bountiful Power: "deal more damage for each boon on you," another example is Chaotic Persistence I mentioned earlier: "outgoing boon and condition duration increase for every boon on you").
Many builds leave room to make use of Mesmer skills with high utility value, Some important examples: ability to pull enemies, wide access to CC skills, various skills reflecting projectiles, etc.
In closing I want to stress that those are secondary goals and you can learn them gradually or as needed, but only after you become comfortable with fulfilling the primary goal.