Assignment

I'm plannig to use Moodle for internet support of a course with approximately 150-200 students and 8 teachers. Nowdays there is a php application used for submission of major homework and online grading but it's a special application developed and maintained by one teacher and it is originally developed for another course.
Moodle is in our interest because of its modularity, continuous development, and web-based administration. There are few features I'm seeking but I have not found Assignment or Exercise or other module posses them:

Is it possible to distribute tasks randomly (as Exercise can), perform tasks offline (as in Assignment), and let students NOT to grade themselves (I don't know how to sidestep it in Exercise) by a single activity?

Second feature is related to organization of our course: There are many classes - it implicates use of groups in Moodle. There are also several different laboratory tasks (each student solves one of them and uploads a report). Is it possible to keep information which student solves which task?  I have two ideas:
1) Student chooses task specification by own from predefined list of tasks - I don't know an appropriate module.
2) Advanced grouping which enables a student to be a member of 2 groups - the first group corresponds to the class, the second one to the task student is solving - this group should be choosen arbitrarily by student. Assignment module would be sufficient in this case.

Do anybody know a way how to reach this functionality in current version of Moodle and existing modules? Is something similar planned to be implemented in Moodle2?

Ota