Yes, CV for everything in BE; in AE, résumé as the more general term, CV only for academic jobs (that is, a résumé plus a list of publications, courses taught, etc.).
>>Wenn due also Zeugnisse mitschickst, in denen deine jeweiligen Tätigkeiten beschrieben sind, ...
>>... vollständige Unterlagen ...
As you probably know, this is the traditional German practice, but in most English-speaking countries, you should not include extra documents. So you do indeed want
>>ein Resume, in dem du für die einzelnen Stationen beschreibst, was du dort ungefähr getan ... hast
That is, assuming it's not obvious from the job description. If all they want is a chemical engineer and you are one, you don't have to write about using computers and working with people. For less technical jobs, you should give more details, not in order to be wordy or subjective, but just to show how your skills and work experience match the particular job for which you are applying. (But don't describe what you learned in school or university; that's less relevant, and more obvious from your degree.)
In this kind of a résumé, details do matter. Most native speakers may be more competent, but maybe you can show that you have lived overseas and passed translation exams. Most 25-year-olds may have more energy, but maybe you can show that you've worked 10- and 12-hour days and traveled on business.
The point is that those are specific skills and areas of work experience, not just saying in a general way, 'I love your company and think I am a great fit for this job,' or 'I am hard-working, detail-oriented, and a team player.' You shouldn't really put that kind of empty filler in an English résumé either, and most sample résumés and jobhunting advice books won't advise you to, unless it's really a low-paying, entry-level job where the résumé probably doesn't honestly matter that much.