Well done on getting the job!
Previous members have covered where EO ranks, but there are a variety of job roles for each grade as well. Typically pays the same, but Work Coaches tend to get a bit more than a lot of other EO roles across CS.
What jobs can you do after EO? Basically, almost anything you like. As long as you can write good examples that meet the criteria for the job and success profiles, and of course, come across well at interview, then you can apply for anything on CSJ like you already would. One perk is that some jobs are internal only so you will gain access to these once you link your account with your CS email. Some jobs might require specific essential criteria or experience, such as some Fraud-related roles needing knowledge of their system or some Digital roles needing coding experience etc etc. But these jobs tend to be less common overall, the vast majority of the roles you can just apply for with your experiences gained in work/life.
If you are the kind of person who will reflect on what you have done, how you can improve, what you'd do differently, and seek opportunities then progression is definitely there. In the CS, you will not just get progression naturally - you have to apply on promotion and recruitment is always fair and open. This is why you will need to constantly work on your success profiles and build examples so you can apply. You will get to a point in most CS roles where you are very competent at the job and there may not be the opportunity to improve that much more, so you may need to seek advice from leaders and look at shadowing opportunities or taking on other responsibilities to develop. You may need to be a little bit selfish in this and also aim to use some of your free time to focus on your applications and techniques. In my experience, you need to treat applying for jobs like another job in the CS - it takes a lot of effort and commitment to get good at the applications and interviews, it is more about that than the actual job. You need to understand how to demonstrate how good you are and what your potential is.
Survival tips... I would say, take on board as much of the training as you can and understand what the role is. Assuming you are going to be a Work Coach? This job can be rewarding, you will meet some amazing and lovely people, but also some people who are not so nice and aren't really interested in looking for work. You need to understand that you are dealing with some of the most vulnerable people in our society and there will always be challenges. You'll get good support, but sometimes it is difficult if you have crying customers who don't know how they're going to feed their children, people with severe medical conditions, people who might be suicidal, people who may not speak English... Everyone is an individual with their own circumstances. The best advice I can give is to learn to read people, ask the right questions, understand what they need, and figure out how best to support them. The job will vary and you have some control over your diary as to when you book appointments. This will all come with time and experience.
I know this can sound a bit scary, but I did the Work Coach job for a couple of years and it was great. It isn't something I'd want to do for a decade, but if you are going to work for DWP I think you should do this job at some stage as it will give you the best overall picture of DWP and help you have an understanding of our front line and customers to benefit you in future roles. Again, just build rapport with your customers and you'll figure out how to structure your day and what to do. You'll get people who apply for plenty of jobs, need little support, and just have a quick 10-minute chat about how it's going. You'll get some people who you know are blagging you and aren't doing much, but will turn up for every appointment and say enough (even though it might be like pulling teeth sometimes)! People who are 'woe is me' and don't think they'll ever work... You just need good people skills, you can only do what you can do. Understand when to draw the line, when to refer to other places, you're not a doctor or psychiatrist etc.
Offices will vary, and local practice will always be a thing as will local labour markets and types of customers. You might work in an office where there's a higher population of customers who do not speak much English, or a higher rate of ex-offenders as some examples. Team Leaders will operate differently by site, some offices may have cliques, some may use hot-desking, some may have a set desk rota... It just depends. I'd just always speak to your team leader if you find yourself not wanting to sit next to someone for whatever reason. All of your last points just can't be answered properly really, it will differ.
Any other questions, just ask! Last thing I'll say is be strong if you end up with something upsetting early on. It is going to happen to someone where one of their first appointments is an angry or suicidal customer and you can't let this affect you too much. Just do the best job you can. I know I have mentioned things like this and they are very real, but they are of course less common than a nice customer looking for work that you have a lovely chat with