How do you play this note on the piano that is circled in red (lower right corner of the sheet).
1) There is both a flat and a sharp notation (wouldn't they cancel)?
2) What do the four dots mean?
This notation simply means that you are to play the given four pitches simultaneously. From bottom to top in the right hand:
E G Bb C#.
The reason there is a separate flat and a separate sharp is because they modify different pitches: a B in the case of the flat and a C in the case of the sharp. (Notice how the flat is centered on the middle line for B while the sharp is centered on the space right above that.)
And the four dots mean that all four of those pitches (which have a stem, thus they start out as quarter notes) are actually dotted quarters, so they will last the entirety of the measure. These dots, if you don't know, add half the value of the preceding entity. So if the preceding entity is a quarter note, the dot will add half of that value (an eighth note) to that quarter note, creating a dotted quarter (worth three eighth notes in duration).
As noted above, this is a chord,
E G Bb C# or bunch. Looks like an
E diminished 7th and all notes should be played simultaneously and held for a 1/4 beat plus 1/8 which equals (3/8), or a whole bar in your 3/8 example.