As you mention, 1 is already true.
Your 2 is certainly planned for the future version. The author will have control over whether students can go back or not, whether previous parts will allow answers to be resubmitted, and whether parts "accumulate" (so they all show at once) or only the active part is shown.
Your 3 is a good suggestion, and I will add it to my list or requests.
See http://webwork.maa.org/moodle/mod/wiki/view.php?id=164 for more about the compound problem plans.
Your comment about going on to the next part is certainly one that I have heard before, but because of he way that WeBWorK works internally, it is not possible to do as you request (at least not without major changes to PG). The reason is that the text of the problem is generated BEFORE the students answers are checked. Indeed, as the problem is processed, the text is created, and at the same time, the correct answers are determined, and the answer checkers are assigned to them. All of that has to be done before the student answers can be checked. Then the answers are checked and the grader is called to determine the final score. Finally, the answer result table is placed at the top of the page.
So the point when we know whether the student's answers are correct or not doesn't occur until after the text of the page is created. The text that shows up must be the text that goes with the answers that are being checked (not the answers for the next part). This is the reason for the second submit. I understand that it is undesirable, but I don't see any practical way around it within WeBWorK's current problem framework.
See http://webwork.maa.org/moodle/mod/forum/discuss.php?d=5834 for more details.