Since I am an editor and have taught English to non-native speakers, I have taken the liberty of annotating your posts.
Hi, I am not an English native speaker . . . .
a native English speaker
I have an instrument which can be used for sampling of gases.
for sampling gases
Originally the sample inlet is a hole with an inside diameter of 1.6 mm.
A hole is an empty space within a surface or an object, so if it is a round hole it has only one diameter. If you're speaking of a more complex construction like a nipple or a tube, which has both an inside and outside diameter, then you should call it what it is, rather than a hole.
The manual book is in German . . .
The manual is in German
. . . . so the English term . . . .
A "term" is very short, one or two words, three or four maximum, describing a single concept. "The term for the feeling you described is 'anxiety'." "The term for that twelve-beat dance music rhythm with very little syncopation is a 'country shuffle'."
What you're describing is a
phrase, or even an entire
sentence.
An additional stainless steel T-joint was place . . . .
This is the past perfect tense so it must be a past participle: "was placed."
. . . . which originally is a hole with an inside diameter of 1.6 mm.
No, the inlet is not just a hole in the T-joint. The picture shows it to be a fitting. There's probably a better word than "fitting," but I'm not an engineer so I can't think of it. A fitting has both an outside and inside diameter, and there is, indeed, a hole in both ends.
Then, I want to continue with describing what I did with the T-joint: "One opening of the T-joint was connected to the original sample inlet, the opposite opening was connected to a 1 m teflon tube connected to a nitrogen tank, and the third opening which is perpendicular to the other openings . . . .
Use commas here: "the third opening, which is perpendicular to the other openings." But more importantly, this is a little difficult to read. I had to read it twice to make sure I understood it. It's not the English translation that's the problem, it's the geometry. You start with "one opening" and leave the reader guessing which one it is. If I look at the picture briefly and imagine that you're starting with the one at the top of the picture, I get confused quickly. You might just say, "the opening on the left in the illustration...", although, again, I would just say "the fitting" instead of "the opening," or whatever more proper term an engineer might use for that particular kind of fitting. I automatically assume that when you say "opening" you actually mean the hole in the fitting, when in fact you're talking about the fitting itself.
was capped with a septum and served as the new sample inlet".
In English we usually put the period inside the quotation marks, not outside.
. . . . I do really trying to write . . . .
I am really trying. This is the present progressive tense. "Do" as an auxiliary verb takes the infinitive: I do try, she did try. "Be" takes the present participle: I am trying, they were trying.
. . . .there is somewhere written in the "instruction for the author",
somewhere in the "instructions
[I'm sure that was plural)] for the author" it was written,
whenever I use an abbreviation, I must explain what is the full phrase of the abbreviation . . . .
whenever I use an abbreviation, I must define it
when it first appears. -- "Firstly" is not a real word. Some people use it, and our democratic American dictionaries have started to list it just like they list "snuck" and "dove" (the verb, not the bird) but they're wrong.
Of course I have no problems writing for example . . . .
I have no problem
. . . . can I just write 1.6 mm ID stainless steel? Also for OD (outside diameter).
I'm not an engineer but even I know what ID and OD mean. Nonetheless, I would hope that the rules for authors would include this one. Speaking as an editor, when in doubt, it's better to provide something I don't want than to omit something I do. It's a lot easier for me to delete words than to write them.
And whether I have to use capitalization for stainless steel (Stainless Steel) or not?
It's not a trademark like Teflon. Many words originally were trademarks, like Aspirin or Heroin, and when the trademarks expire (or in the case of aspirin and heroin, stolen from Bayer A.G. as the spoils of World War I), people are already in the habit of capitalizing them and don't realize it's time to stop.
Which one is correct: "it eliminates the need of oven and vacuum", or: "it eliminates the need for oven and vacuum"?
"For" is correct. As you study foreign languages, one day you will realize that prepositions have almost no meaning, and the choice of the correct one is simply a matter of tradition. You have to learn each use of each preposition (and most of them have twenty or more uses) individually. I always joke that the only purpose of prepositions is to help us identify foreign speakers.

Why do we say "in English" but you say
auf englisch ("on English")? It's almost random!
I want to say in my conclusion "the proposed method is ovenless and vacuumless". Can I use those words to convey my meaning in #3?
If we didn't know you were German, we'd know it now! That is the German way of forming new words. Of course we do it in English too, but not so freely. We can't make one up for a particular situation, it has to be a consensus of the whole country. Look in Dictionary.com and you'll see that ovenless and vacuumless are not real words. (My spell-checker just told me the same thing!)
If you're speaking colloquially, you can make words up so long as you're certain that the person you're speaking to will understand you. But don't do it in a university paper. I would not allow it in the documents I edit.
You'll have to find another way to say what you want to say. It's better to stick with "the proposed method eliminates the need for an oven or a vacuum." (And don't forget the indefinite article, although since "vacuum" is not a
countable noun you might get away without using it there.
Or is it "oven less and vacuum less"?
Definitely not. "Hopeless" and "hope less" do not mean the same thing!
Or, "oven-less and vacuum-less"?
If you're inventing new words in a letter to a friend, you could spell them that way. But not in a university paper. If you are a respected expert in your field and your research is going to enrich civilization, then you're allowed to invent new words, so you could write "ovenless" and "vacuumless."
Using a hyphen is more acceptable if you are actually joining two words that can stand alone. "Sugar-free" and "labor-intensive" are okay because both "free" and "intensive" are words. But "-less" is just a suffix. (Yes, "less" is also a word, but it has a different meaning than the suffix.)