Is that correct, that I put the present tense (states) and afterwards I use the past as a subjunctive (were, needed)?

No. Everything here should be in the present tense:
Mustermann states that all plants are green and need sun.

Your second example I would rewrite as follows:

Spokespersons from all committees stated that service X has been very good since company Z has been in charge.

Thank you! So no subjunctive at all in the first example? More easy for me :-)

How would you write it in cases where I don't put the author like "Mustermann states ...", but write it like:

Alle Planzen seien grün und bräuchten Sonne (Mustermann, 1998).
In that case it seems wrong to me to put the present tense, since some guy stated that, but might be that red plants exist too...

Or for example I have this sentence in my analysis:
Supply by private gas vendors was irregular and at high prices(Interviewee C). How do I manage in English to express that its not a general truth, but something that somebody states?

If "since" means "seit" rather than "da", the original (unreported) direct quote is wrong.

And this is the simple past (or preterite) in English, not the subjunctive. When used to "replace" the present in indirect reported speech, we often talk of "backshifting" (it also means that an original simple past tense becomes a past perfect).

In English, you should introduce indirect reported speech in some way. It is this introduction (rather than subjunctive mood) that tells the reader that the speech is reported.

yes, I read that about the backshifting, but my original sources are quite often in German or Spanish (like for example the direct quote I put). So how do I shift that back?

What would be the subjunctive then?

Die Form gibt's so nicht im Deutschen. backshifting braucht man nur, wenn das reporting verb in der Vergangenheit steht, also 'Mustermann said that all plants were green'.

Indirekte Rede im Präsens muss im Englischen durch das regelmäßige Einstreuen von Verben wie 'he said, he stated, according to him' ausgedrückt werden (was MikeE vermutlich mit 'introduction' meinte). Eine eigene Verbform gibt's nicht.

#5
What Gibson said.

re backshifting
If "since" meant "seit" (not "da") in your quote, it should have read
“the service has been very good since company Z has been in charge.”

In indirect reported speech, this becomes ("canonically")
"Spokespersons stated that the service had been very good since company Z had been in charge.”
In academic or scientific work, I would tend to stick to this form with backshifting (i.e. "has been" becomes "had been"), since there may be no solid basis for the implications of other forms.

ion1122's suggestion
"Spokespersons from all committees stated that service X has been very good since company Z has been in charge. ",
not backshifting "has" although the reporting verb is in the past tense, is good in this example, but I wouldn't advise thinking of it as the standard form, since it may be difficult for a non-native speaker to judge when to use it.

#5 re subjunctive:
Short answer : Forget the subjunctive. It has nothing to do with indirect speech as such.

Long answer:
There are three things that are sometimes called the "subjunctive" by different people.

1. (which everyone agrees on), also called the "present subjunctive" (which is misleading since it is tenseless) takes the same form as the bare infinitive. It is used for instance in subordinate clauses expressing demands, exhortations, requests, etc.:
"I demand that he come [not comes] here immediately."
"I requested that he be [not was] allowed to leave."
2. the irrealis form of the verb be, i.e. were (and no other word). This is very often called the past subjunctive though it is not the past form of the present subjunctive. It is used to express that something is counterfactual or unlikely ("If I were you ...").
3. The simple past (preterite) of any verb when used in a similar meaning to (2) ("If I had a hammer"). This hypothetical past is called the past subjunctive by some. It is also used informally with the verb be ("If I was a wiser man ...).

Woh, thanks for all your answers!!
So, if I do the backshifting as a standard in my analysis,
"Spokespersons stated that the service had been very good since company Z had been in charge.”
Does this sentence express that the company IS still in charge?
Cause as an english learner it seems to me like a terminated process in the past (abgeschlossene Vergangenheit).

Sorry, I never paid attention (or I never had paid attention?) to english tenses when I was in school and now they are driving me mad :-(

Backshifting in English can be a bit tricky. The basic model is:

1. Tom said he was the smartest astronomer ever to peer through a telescope.

However, so-called "eternal truths" are usually expressed in the present tense, even when introduced by a past-tense verb of saying:

2. Copernicus said that the earth revolves around the sun.

Complicating the picture is that published sources are often treated as events in the present, even when the publishing occurred in the past:

3. In his Principia, Newton asserts that all objects attract each other.

Compare #3 with the following:

4a. In his Principia of 1687, Newton asserts that all objects attract each other.

4b. In his Principia of 1687, Newton asserted that all objects attract each other.

4c. In his Principia of 1687, Newton asserted that all objects attracted each other.

I believe all three of the above could be correct, depending on context.

I would use 4a if I were comparing two different editions of the Principia.

I would use 4b if I were making the point that Newton made his statement in 1687.

I would use 4c in a context like the following that underscores the tentativeness of Newton's statement: "In his Principia of 1687, Newton asserted that all objects attracted each other, but he later changed his mind."

Other English speakers may not agree with the above, but that is how I see it.

I basically agree with ion1122.

It is sometimes difficult to express the difference between 4b and 4c, when dealing with what were believed to be eternal truths. The preterite adds "remoteness" or "distance". I would also tend to use the preterite in sentences like
"Thales asserted that the earth was flat".
I would tend even more that way if I added "and he was convinced of it till the day he died".

BTW that example demonstrates why I stressed that backshifting is different from the subjunctive in English. You do not say
* "Thales asserted that the earth were flat".
There are other sentences* where (some) native speakers might get confused, but this is not one of them.

* An example given by Huddleston is
(*) "She phoned to ascertain whether he were dining at the club."

Thanks a lot to all of you! I hope I got it ;-)