1 —
There’s no way to have the due date directly beside the task name, however you can have it directly underneath (where you see “Template” and the author)!
To do this, please:
- Open the object/template
- Place your cursor near the top (above the title), and click on “relations”
- In the menu that pops up, click on the
icon next to any relations you would like to appear under the name of the task.
Please note that the order in which they are displayed, is reflected by the order in which they were starred/added.
If the relation you’re looking for is not in the menu, you can click “+ New” at the bottom, and add any relation(s) you’d like.
If you don’t want the relations to appear under the title, but would prefer them to appear elsewhere, you can drag the relations (from the menu that popped up) to somewhere in the object. This can also be done by typing “/relation” and selecting whichever one you’d like to add.
2 —
Currently, the only way to see the objects nested within another object, is by using the sidebar.
For now, though slightly more time consuming (sorry!), you can add the pre-existing “Linked Objects” relation, to which you can then add the same links that are referenced within each individual object. This will allow the references/links to be seen in your set view. 
@lynxlove has also created a really nice task manager with support for subtasks using a custom “Objects” relation, which you’ll likely find useful!
Regarding your comment on filtering these tasks/subtask, can you please elaborate on what you’d ideally like to be able to do?
Thank you! 