Chord voicing
The ability to produce different volumes for each note within a chord is a core piano skill. The way it works, by analogy: stand with your weight distributed equally on your feet, then shift your weight to one foot, then the other. Note that when shifting weight onto your right foot, for example, you don't press into your left foot to shift to your right, and you don't press your right foot into the ground to create the weight.
This is essentially the same thing as when playing a chord with one note louder than the others, except you have ten fingers rather than two feet. One begins each chord "standing" at rest on the surface of the keys. But as the weight of the hand and arm release into the keys to create a sound, some fingers receive more of that weight than others. Here, whichever finger is playing to top note of the chord will get the greatest weight.
Besides shifting weight from one foot to the other, an additional way to begin learning this technique is to stand near a wall and place one's palms against it. Then lean into your palms, and practice shifting your weight from one side to the other.
Pedal
The absolutely should be pedal throughout the passage. Pedal is generally assumed in Chopin — even in Romantic-era music generally — because it produces a warmer tone than playing without. In this case it also helps preserve the "sempre legato" (always legato) line that Chopin asks for.
