Do operations on indexed views happen in parallel?
It appears to do it in sequence in your plan. Not in parallel. The insert happens into the heap. The inserted rows are inserted into the eager spool which is a blocking operator. When all rows are inserted into the base table the rows are inserted from the spool to the view.

As for the percent issue it appears that the spool confuses SSMS. Despite showing up twice in the plan (with the same NodeId) its cost should only be counted once but it seems as though its cost is completely disregarded when calculating the overall estimated subtree cost for the plan and then it displays the operator percentages as a proportion of this incorrect total.

+---------------------+-----------+------------+--------------------------+
|                     |           | % of total | % of total without spool |
+---------------------+-----------+------------+--------------------------+
| Table Insert        | 0.0100022 | 39.84%     | 50.00%                   |
| Spool               | 0.0051012 | 20.32%     | 25.50%                   |
| CX Insert           | 0.010001  | 39.83%     | 49.99%                   |
| Sequence            | 0.000002  | 0.01%      | 0.01%                    |
| Total               | 0.0251064 |            |                          |
| Total without spool | 0.0200052 |            |                          |
+---------------------+-----------+------------+--------------------------+


SQL Sentry Plan Explorer correctly handles the issue.