iPad PDF reader app with seamless handwritting annotation experience
I found it! Good notes does exactly (1) and (2) 

You can write without accessing menus and browse the document at the same time by using two-finger gestures (to distinguish them from the writing itself). And writing is really snappy.

It also happens to have a great feedback system, so I added a suggestion to add a handwritting calculator.

The only missing features (for my taste) are margin cropping and automatic Dropbox synching.