In chord a construction, in a Adim, for example, is it indifferent to have instead of A, C, D#, have, A, C and Eb?
This is one of the most common misconceptions in aspiring musicians. Saying that because D♯ and E♭ (or any pair of "enharmonic" notes) sound the same, therefore you can choose either one is like saying that because "they're" and "there" sound the same, you can use either spelling. They have the same sound, but differing semantics.
There are probably tons of questions about that on this site already. A quick search, for example, found these:
- Why do notes have multiple names?
- Which enharmonic to use when writing down a sequence of chords
- Using the correct enharmonic equivalent
Intervals are counted diatonically, meaning that a scale will contain one note with each of the seven letters (whether that note is natural, sharp, or flat). A typical chord within that scale will be built on thirds, which means it skips every other letter. So any triad starting on A will have the notes (A, C?, E?). The C and E have question marks to indicate that whether they are natural, sharp, or flat depends on what type of chord you are building. So A minor is just (A, C, E), while A major has a raised third (A, C♯, E), and A diminished will have a lowered fifth (A, C, E♭).
Diminished chords (triads) are made up from a root note, a m3 and a diminished 5.
Therefore, using A as the root, the m3 will be C natural, and the D5 E♭. That's how it's spelled. Yes, on a lot of instruments you could play A, C D# notes, and it would sound exactly the same. But that's not the point. The point is it's called A diminished for a reason. Calling the note D♯ actually makes the interval an augmented 4, so then it wouldn't be a diminished chord!