Do you mean in the links to the TheoryTabs (the gray ones with the YouTube thumbnail)? Or do you mean on the TheoryTabs themselves? If it is the later, we already do this. At the top of every TheoryTab there is a key selector / indicator that is almost exactly what you describe:
3: Are you referring to the piano visualization or the piano audio? Hookpad /TheoryTabs already support 5 octaves which covers > 99% of songs. The instrument visualization is limited to 3 octaves because we wanted to keep it large and easy to read.
Another thing, would it be possible to implement like a second line so that there can be two different notes happening at the same time without using chords? E.g like a right hand and a left hand? Again not needed for most tabs but for most piano pieces there are usually arpeggios of the chords played by the left hand and the melody by the right? Thanks!