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All the music pieces and songs are written on some scale, say if we consider D major scale the Cs and Fs must be sharp and others natural. But the Cs and Fs in that piece might be flat or natural at some points as well, or some other natural notes may be sharp at some point. So if we don't write the piece using only D major scale notes, what does it mean for the piece to be in D major? we could even change the signs without changing the melody and hence change the scale as if it does not really matter what scale we consider for the piece, am I right?

Also, when some music is on a pentatonic scale, is it the same? can we use other notes than the ones in the pentatonic scale, or should we just use those five notes?

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You use on, but should it be in?

Music is never written on a scale, or even, for that matter, in a scale. Tonal music is written in a key. And, yes, often other notes are used as well (although rarely C♭ or F♭ in key D!).

The key provides a couple of things - one, the likely notes that will fit together best, and two, a clue as to where 'home' will be expected. When we see two sharps at the beginning of a piece, most of us would guess that it's likely to be 'in key D major', or 'in key B minor'. Those are the usual suspects for 2♯, and it helps the reading a lot.

It could, of course, actually be in E Dorian, or A Mixolydian, which would use the same sharps, but then 'home' would be on a different note for each.

Those accidentals you mention are often there to facilitate a modulation, or key change, but usually remain as accidentals unless there's a complete and utter key change, in which case, the key signature should change to signify a different set of notes - key or scale.

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