Does David ask to be afflicted in Hashem's anger?!
Radak: No. "Lo" written above refers to also to this. We find like this - Tikvas Aniyim Tovad La'ad" (9:19).
Malbim: He asks that there not be both rebuke of Ketzef and afflictions of Chemah (they are different; refer to 38:2:2:2). He was suffering both; he thought that one of them suffices. Inner rebuke and great regret should remove the external afflictions; or great external afflictions will bring regret in the heart to atone for the sins.
Is "[Al] b'Ketzpecha Sochicheni" the same as "uva'Chamasecha Seyasereni"?
Radak: Yes. The verse repeats the matter in different words.
Malbim: No. I explained above (regarding "Al b'Apecha Sochicheni v'Al ba'Chamasecha Seyasereni"; refer to 6:2:1:2) that Af and Ketzef are exposed anger. Chemah is hidden in the heart. Tochachah is to prevent sin in the future. It is not with Chemah, for an enemy does not rebuke. Sometimes it is with great Af. There, David requested that it not be with anger, rather, with soft words. Yesurim are for a sin in the past. It is always with exposed anger. David requested that it not be with inner anger. Here he requested differently (refer to 38:2:1:2).