Q:

Grouping or visually linking multiple rows in tabular data - best practices

I need to help users interact with a (potentially very long) assignment list of healthcare procedures. The list is tabular data that users want to sort in various ways. 
Since this is healthcare a patient may have multiple procedures at the same time. Therefore we've discovered that users frequently need some sort of grouping or linking of the data rows to "work on" related items. One catch is that rows often must be sorted by an attribute like due date, physician, etc.
Finally, users may take individual items off the work list (eg begin a process) without taking the entire group. We currently have tabs for "unassigned", "assigned to me" and "complete". The plan was to decrease the size of the list by segmenting it that way. Groups would potentially have children in each tab.
On the plus side, this is only available on desktop browsers so I get plenty of screen real estate and no mobile issues.

In this example elements, 2,8,9 (blue dot) could be grouped or linked as they're the same patient & procedure date.
As I'm building out a prototype, I'd take advice on any of the following:

What are the best practices for visually grouping tabular data? Background color? Icons?
How do I handle sorting by child attributes that may break the grouping?
When viewing an item detail, is it advisable to allow users quick access to other "related" items?
Suggestions on how I deal with groups that cross status tabs (see above)?
Are there examples of this that anyone could point to? I'm struggling to search for the problem.

A:

You can have 'soft' grouping with colored elements, such as icons, or 'hard' groups as separated tables. Or both, like in this example.

Alternative color tag groups:

