Howdy Ralpheo,
It sounds like you're quite adept at moving around in sequencers, and you're right that Composer is set up to deal with issues such as quantization in a different way than a sequencer does. You'll probably find the Piano Roll feature to be more familiar territory for adjusting attacks and durations of performance.
In Piano Roll, you can
1. edit the performance in conjunction with the notation (select the "Edit both" button on the second palette),
2. edit only the notation and keep the performance "as is" (select the "edit as notated", to keep the "feel" of a performance but clean up the notation) or
3. edit the performance and leave the notation as it is (select the "Edit as performed"), so you can add specific "feel" to a performance without affecting the sheet music notation.
There are also tools for "snapping" the performance to the notation (eg. snapping the attacks of selected notes to their notated attack locations, or snapping the durations) that you'll probably find helpful as well.
You can also shift the performance (or notation) of selected notes to give the feel of being "on top" of the beat, or a more laid-back "behind the beat" feel.
You can jump in and just try out this feature, or you can read more about it in Help/Users Guide, and use the Index to look up "piano roll."
Have fun!
Sherry