Which "natives of the English language" do you have in mind? I ask this because you use the before the quoted noun phrase above. And when a native English writer/speaker uses the, we are making a definite reference to something. When we make a definite reference to something that is a plural noun phrase, we almost always have a specific group in mind, AND we usually expect that our hearers/readers know which group we are talking about. But here I have no idea which group of native speakers you are talking about.
If you use no article (also called the zero article) before "Native speakers of the English language", you are making an indefinite reference and do not have a specific group in mind; you just mean native speakers of the English language in general.
As far as
My cell-phone is on silent mode.
First, it would not matter if there were 10,000 available modes. You would still not use an article. Each mode is already unique.
This is similar to a location where there could be one million tables, and you would say:
My cell-phone is on Table 6852.
And we would not say the Table 6852 even though we have a definite table in mind. It is basically the name of a uniquely identifiable table. And silent mode can be considered a uniquely identifiable mode. Just like Stack Exchange uses User##### to uniquely identify users. We don't need the definite article before one item/user/table/mode that can be uniquely identified from others in a certain set of items/users/tables/modes.
As for the preposition, on is definitely the one to use, because it fits with already established uses of on.
You can shorten your sentence to
My cell is on silent.
My cell is on vibrate.
My cell is on loud/ringer.
Just like
My TV is on mute (mode).
My speaker/volume is on low (mode).
The heater is on high (mode).
And you can instruct someone to put their phone on vibrate or their TV on mute.
Using in instead of on in the above sentences sounds bad.
Note that a person can also be on hold--not in hold--when waiting for a person to talk to.
Ultimately, it's just a collocation that doesn't require either the definite or indefinite article. We have lots of those, including
I'm on top of the world.
The shot is on target.
The actors look better on screen than face to face.
That football player is on fire; he's scored goals in seventeen straight games.
We have collocations with in (stand in line) and at (be at school) also, but this answer has been long enough.
This answer addresses the two questions at the bottom of the body of your question, but only tentatively addresses the question in your title.
The grammatical construct where the article is missing appears to be called the zero article. There is also a book written about the zero article.
One might have thought that zero articles are used when the noun is inherently unique, since there is no need then for an article to distinguish any one of many from a specific one of many. However, English is inconsistent here. One example that has come up in a similar discussion is The Eiffel Tower. Another example (from the book, IIRC) is The Baltic Sea. In both cases, the noun is unique but the definite article is part of its name.
One suggestion is that we always use the zero article with names. In examples such as The Eiffel Tower and The Baltic Sea, the word The is considered to be part of the name rather than a separate article. Street names are similar. For example, "Where is Main Street?" has no article but "Where is The Strand?" does because The is part of the name The Strand. Note that this doesn't cover all cases since "I can design an Eiffel Tower" and "I can pave a Strand" are arguably acceptable. In many cases, though, this 'rule' holds.
In the case of your question, Room 401 is the name of the location, but the location is not so grand as to warrant having "The" as part of its name. The definite article is therefore not used before Room 401 in the sentence in your question's title.
Best Answer
The article goes with language, so the following work as noun phrases:
The following doesn't usually work as a noun phrase referring to the English language. It would more likely be interpreted as referring to the English people:
Take a look at the following example sentences:
Examples 1c is wrong. Example 2c is wrong in most situations. Example 1b sounds strange; we usually only say "the English language" when speaking about the language in the abstract or as a whole. Saying "English" always works, though it doesn't always sound as nice:
Both examples are acceptable, but example 3a sounds better.
Of course, there are other situations where you'd use an article with bare English, such as in the phrase the English of Shakespeare, but you can do that with any proper noun (see this answer). And if you're using English language as a modifier, it doesn't need an article because it's not functioning as a noun. In the following example, English language is inserted into the noun phrase a Q&A site as a modifier:
The article an belongs to site, not to English, language, or Q&A.
＊ means I think this utterance is unacceptable.
？ means I think this utterance is questionable, but not as bad as those marked with ＊.