Dear Patrik Olterman,
I am not all that well informed about all the functionality that moodle is now able to provide but, an ignoramus responds to the best of his (my) ability....
I think that custom skins for students do not exist yet. They may be coming in the next, or the 2.0 version of Moodle which is placing an emphasis on providing templates governing site display. I am not sure it will be so fine grained as to allow different skins for different users but I think that there is a good chance that it will allow different skins for users and teachers. This work is, I think, in progress. There is a chance that the site templates that in progress are not fine grained enough to distinguish users from teachers but this seems unlikely. Either way, since this work is in progress, I think that it may be difficult to get involved in. perhaps.
I am pretty sure that the calendar does not yet merge with all the other activity modules such that it reflects all their due dates. A nice idea. A lot of work. I think that this is too nice even to hope for. It would require modification to every module such that it communicated with the calendar to include events for the right people. (but for all I know this functionality exists! I don't think so)
I am not sure what you mean by a button to hide assignments that you have already given feedback to. I am uniformed. Sorry.
Alas there is not a teacher task list showing all the activities requiring feedback. I guess that a *global* teacher task list accumulating all the teacher tasks from all the activity modules may be a long way in coming. But perhaps a teacher view for each module, e.g. a view for the forum module may include this functionality sooner - with some way of changing the teacher view to show postings that have not been replied to, or have not been graded. I have wished for this one (in the wrong place - i.e. not on the bug tracker, myself). Very nice! Yes please! My own entirely personal vote would be that you have a go at the this one first, since it seems less complex, and I want it! I often use forums for homework and then I am not sure which postings I have already replied to.