1. Yes, it will be possible to build a badges plugin by combining an event module (which detects when certain events happen) with a content module (which can display the badges, I imagine in place of or alongside the user title). This would be quite a complex plugin which would also manage its own database table.
2. Yes, it would be possible to create a system for tracking users' notifications by combining an event module (to track events relevant for each user) with a page module (to display the notifications for the user).
3. Based on the feedback on this site, dynamically loading comment forms didn't make the cut this time round, but I'm very aware of the issue and it's even started bugging me on the Q2A Q&A...
4. For widgets I'm thinking of the following. The widget will specify where it can be displayed in a broad sense, i.e. left side, right side, across full page. The admin can then determine more precisely where the widget appears (e.g. top of page, after title, bottom of page, sidebar, etc...), in what order relative to other widgets, and on what pages (by matching against the request with wildcards). The widget will be told where it is displaying its content, and on what page, and will simply output HTML as appropriate.