Coaching credentials:
~What does it take to get them, qualifications, courses, tests, etc.
I'll mostly let a real coach answer your questions, but if Bama refers to an African city, where I think it is, not many people, if any, on this board, will know what rules apply.
In the United States, there are a variety of credentials for teaching group lessons (within ISI or USFS syllaba), for private lessons, for coaching at competitions of various levels within ISI, USFS and ISU, and for judging tests and competitions within ISI, USFS or ISU. 4 different organizations give credentials of various sorts:
(1) The ISI (Ice Skating Institute).
(2) The USFS (U.S. Figure Skating, formerly and still sometimes called the USFSA [A=of America])
(3) The ISU (Ice Skating Union, an International Body). I think the main route for ISU Credentials for U.S. coaches is to first get USFS credentials. But it is possible some well established skaters and coaches from other countries who coach in the U.S. have been able to bypass some of the USFS training requirements.
(4) The PSA (Professional Skaters Association). To some extant, PSA training is needed for USFS credentials, and possibly for ISI credentials. Their entry level training is purely on-line, involves some memorization, but requires no skating skill or teaching experience. (In principle the USFS Basic Skills Instructor's Manual says a coach should be able to able to demonstrate the skills they are teaching, but this is not checked. I'm not sure about their high level training. But you need a reference to get in to the PSA. A lot of skaters are picked by their current coach, or a rink, to help teach their group lesson program, and take entry level PSA training to get certified for that, so at entry level certification isn't all that hard.
Different rinks and skating clubs have different requirements on who can coach at their rink.
You can theoretically become a USFS Basic Skills instructor without any training or skill. All you need is for a program manager to say they want you to teach, and for someone to pay $32 to the USFS. I volunteer as an instructor at a rink where some of the instructors only have hockey experience, but still teach entry level USFS figure skating classes. (Hey, how much knowledge do you need to teach "March, Glide and Dip"? And some of these people are very good at teaching.)
Various organizations also give out "ratings", based on a combination of other credentials and how well your best students have done in tests and competitions.
Beyond that, you need insurance in most teaching programs at most rinks, but not all.
It is fairly difficult to get credentials, beyond the most basic levels. As with all teacher certification programs, credentials do not correlate all that strongly with teaching ability, but they serve a useful purpose to the organizations that give them - they make money for them! They also serve to keep out those who aren't truly dedicated to getting them, which is why figure skaters have been willing to tolerate this unwieldy system.
You also need to pass a background check. (At least you have for the past several years, in part because there have been problems with some coaches. They probably look for felonies, and for signs that you might be a threat to children.)
There is sufficient money involved paying off the various involved organizations that some coaches who only teach on a very part-time basis complain it isn't worth it.
There are some small ice rinks that don't require credentials from any of the major organizations. By the way, most ice rinks in the U.S. are themselves insured through the ISI or USFS - but not all. There are many other insurance companies that insure a few rinks.
You didn't used to need accreditation to teach hockey, and most of the coaches are still just parents of would-be hockey players who used to skate. But now various hockey organizations give out credentials, and most hockey clubs require them, in part because they include a background check, and in part because organizations like USA Hockey require their own credentials. That said, hockey players are free to take lessons from other coaches, such as figure skating coaches.
I have no idea whether there are any credentials needed to teach speed skating. I also don't know much about roller and in-line skating.
BTW, many people teach skating associated lessons off ice (e.g., ballet for figure skaters, off ice exercises, choreography and music), as well as various medical specialists and skate technicians (skate fitting, modification, sharpening, for which there are no universally recognized certifications). In many cases, these people have little knowledge of or credentials for skating. (Medical specialties of course involve their own non-skating related training, credentials and insurance, specified separately by each state.) Nonetheless, the best people are often well recognized for their previous work within the skating community.
Beyond that explanation, you need a real coach and/or judge to answer your questions.
~Can a skater be actively competing and have coaching credentials at the same time?
Yes.
It's always been OK within the ISI. Within USFS (and therefore within ISU) it's been OK for the past 15 or 20 years (?), but you have to give the USFS and the PSA their cuts. Cuts aren't on a per-student or per-lesson basis, but there is a fair bit of money involved for certifications, professional memberships and insurance.
Many competitors teach to help support their habit, and as practice for what might be their future profession, or because their coaches want them to assist teaching.
In other words, in the U.S., there are no simple rules about these things. And each country makes its own rules.
P.S. I'm not a coach, unless you count the volunteer BS instructor thing. I don't have the in depth knowledge to fully answer your questions to the level you want. Someone else would have to provide more info.