This would likely be better off reported in the Tweaked thread...
But, w/ the CNN freeze up (was this an app or website? Reading text or watching video/listening to audio?) was there any FC at all? What kernel were you using? What version of Tweaked were you running, and what sort of options did you have installed? A logcat of such an issue would be immensely helpful
Also - were you charging the phone and have the MIUI battery bar active? On other phones I've experienced issues w/ video playback and that combo.
Turning screen off makes music player unusable - what do you mean? The long-press volume controls weren't working? The music stops? What app were you using to listen to music?
Very slow to wake - is there anything more specific you can offer here? Like an amount of time it takes to wake? That really shouldn't differ from stock at all - and there will always be a bit of lag there (though I never have anything more than a second or so).
And fwiw TSMParts is regrettably not an independently functional sort of apk. It requires a bunch of other edits throughout aspects of /system to actually work. But man that would be nifty