What Notes does Trumpet play?
"All of them"... at least in the sense that, like almost all tonal instruments, a trumpet can play all seven pitches of a diatonic scale and all of their accidentals (sharps and flats.) Most tonal instruments can play pitches over many octaves; the playable distance from the lowest to the highest pitch is known as an instrument's range.
There are different types of trumpets, each with a different range. The most common trumpet being the Bb trumpet... According to the wiki:
The standard trumpet range extends from the written F♯ immediately
below Middle C up to about three octaves higher (F♯3 – F♯6).
Traditional trumpet repertoire rarely calls for notes beyond this
range, and the fingering tables of most method books peak at the high
C, two octaves above middle C
It can reach higher notes still but, playing in the trumpet's extreme upper register is quite difficult and not for beginners.
Also, be advised that some trumpets are transposing instruments, meaning written notation does not correspond to the sounding note produced by the instrument.
Finally, it is advisable that you take some kind of formal training... even if it is just a few lessons to get you started. While self-learning is in no way impossible, it can be a bit difficult (especially if you are starting from absolute square one.)