Redmine

Assigned to dropdown schould be dynamically populated depending upon the Trackker.

This is possible currently only per category, not per tracker. You can see discussion on #482 (default 'assigned to') to add more functionality.

We need to modfiy the UI of New Issues as we need to add more sections to the New Issue form.

If you mean more sections as in custom fields, head into administration and click 'custom field'. Once field created, assign it to trackers, and then enable it per project basis (unless you make it for all projects).

Can Draft functionality be implemented ? To save the details of issue in different table with status as draft and will be visible to the User who as created it. And once it is submitted it's status is changed.

You can make it that certain roles make a status 'draft', and automatically ticket gets assigned to someone who can change from 'draft' to, say, 'assigned'. This is part of tracker/roles/status workflow setup.

Can we customize workflow depending upon business requirement?

Yes, you can setup your own workflows. It kind of becomes tricky with projects, as you will need to enable different trackers for different projects to maintain separate workflows, but otherwise, all good.

Please in future: read documentation, go to forum.

Kind regards