to answer your questions.
1) "Yes", the travel agency would be the service provider. They are offering a b2b service with details about their hotel offers. It doesn't matter who coded it, a freelancer or the company itself. But "No", I doubt very much that the error messages are intended for the freelancer or IT company that coded the service (in your eyes, Service Hersteller). Most companies have pretty strong barriers between developers and operational staff. You really don't want developers, or a foreign company to have access to your production environment. In fact, it's almost a taboo.
2) Without seeing your document, I can't judge exactly what the original authors intend with certain terms. There are definitely overlaps in terminology that are possible. I can also not judge whether there are multiple steps in a plan to achieve something. What you described as occurring in your document, the cycle of integration, test, feedback (code changes) then back into integration.....is indeed the normal development cycle for computing projects. This cycle may be embedded in a governing project philosophy such as "agile" or "waterfall". When I read Integrationsschritt, I'm thinking of some defined goal. For example, one step along the way for integration is to improve the error handling and error messaging of the code. This Integrationsschritt might be that step. A following step might the integration of these error messages into a new operational tool, that governs the running programs, with the intent that some operator seems a flashing red button when a pre-set number of error messages occur. Another step might be automatic responses to the service provider saying for example, "we requested information about hotels in Berlin and received zero results. Is your service working properly?". As such, I really don't think that the Integrationsschritt is comparable to a cycle. It seems much more like a predefined set of tasks that achieve a particular milestone on the way to a final goal.
So perhaps you could use release or milestone as a synonym for step. But perhaps these terms are used in your document elsewhere.
p.s. I tried sending you a pm before, but the system wouldn't let me use your name "Meiki_zett", so perhaps your username is different to your nickname, or you have that option turned off. Anyhow, without trying to be rude, I get the feeling that you're quite unfamiliar with some of the terms in the jargon-filled world of IT. If you need someone to proof-read your final work, or work-in-progress, then send me a pm and we can come to some arrangement.
p.p.s To the regular users, I'm not sure if this offer contradicts any etiquette rules here on the site, it was meant in a well-intentioned way, and I would only offer my services when I thought that my specialist area of IT is needed. Please inform me if I have unknowingly contravened any etiquette rules here.