Beethoven "Moonlight Sonata" 3rd - How to read 32 note rolls

[xr280xr]

I'm nearing the end of Beethoven's "Moonlight Sonata" 3rd movement and I'm not sure how to read the few measures like the one attached. I'm thrown by the notes having two stems. The upper stems seem to indicate they accelerate, 8th note, dotted 16th, 16th, 32nd, but the lower stem is all 32nd notes. Are they played evenly or is each note shorter than the previous? If each note is shorter, it's so fast...do you more just kind of "eye-ball it", for lack of a better term, than count it out and play it perfectly measured?

And a really beginner question, when a note is tied to the same note, or a chord is tied to the same chord, do you play the second one, or just continue to keep the key(s) pressed? Thanks in advance.

[brogers70]

You just play each note, one after the other, as though they were all 32 notes, but you keep the keys depressed until the end of the chord. It's a very precise notation for something simple; rather than just having a vertical squiggly line to show that the chord is arpeggiated which would not tell you exactly how fast to arpeggiate the chord, Beethoven gives you the details. It's simpler than it looks.

[xr280xr]

Ahh, ok. Thanks!!

And a really beginner question, when a note is tied to the same note, or a chord is tied to the same chord, do you play the second one, or just continue to keep the key(s) pressed?

Now that it's not 4 am, I feel like I definitely know the answer to this, but I was just having doubts because it seems like some of the pros I've watched playing it re-strike some of the notes that are tied in this piece.