Oh, the single most important thing with fast rhythm and shred is to start SLOW, and I mean SLOW and build up gradually to the speed you want it to be.
this is probably the most important thing, just remembered that when I was new I used to play bodom riffs, leads and a few solos, no where near full speed but it was good practice
another thing on alt picking, after tremolo picking speed, the next thing to limit speed is string skipping and is the thing that messes me up if I ain't warmed up properly or I'm just having a bad guitar day as a whole
recently restarted practising going up and down scales across the neck in groups of 4, fantastic for both hands