Notes too far apart

It is a tenth (the one in measure 4... prohibitive)... not everyone manages to reach it. The small note indicates an alternative solution to the one preferred by the composer; he writes the notes small because he knows that the solution he is looking for is very difficult to demand. In this case, however, it seems to me that the value of these little notes is different.

In any case, I would arpeggiate the first chord of every measure and, helping myself with the sustain pedal, I would repeat the note of every half-measure

Which piece is it? Is it a reduction?

It is about "Ob la di ob la da" by the Beatles.

I don't know what a reduction is...

In other measures I played the highest note of the chord with the right hand, but here it's just not possible.

I had also thought about moving the A of the first chord in the bass clef up an octave to play it with the right hand, or perhaps not playing it at all, but I don't know...

The score you are using is a piano reduction of a piece that, in fact, was not written for the piano... when you listen to the song, what instruments do you hear?

Practically, it is a synthesis of the sounds of the arrangement... to play it on the pf [piano], one must manage (excuse the pun) as best as possible... namely: resonance pedal at will)

Typical light music notation... it is just a sketch of the fundamental and characteristic parts of the song. You can also take the melody and develop the chord symbols indicated.

besides, both the melody and the chords are wrong... perhaps it would be better to look for a more correct edition, even if simplified.