Is it possible to set the warning level for TODO / FIXME in Pycharm / IntelliJ?

AFAIK – No.

You can change color of markers on scroll bar .. but unable to add (or change, if it has any) severity.

IntelliJ has a severity for todo comments (double click on hector, under Code maturity issues there's an option for TODO comments). Not sure if it really does what you're looking for and if it is present in PyCharm as well.

Double clicking Hector in pycharm does not lead to a TODO option.  What I really wanted was two levels.  There may be dozens of "TODO later", and a few "FIXME now" items.  So one should be a severe error, the other a warning.

Sorry, I just assumed that this part is identical to IDEA but maybe that inspections is only relevant for a java context. How about the following:

You can define several patterns for todo items (at least in IDEA). Open the todo dockable frame and click on the blue filter. There's an Edit filter popup menu (or go to Preferences > TODO). You can define multiple types of todo patterns there (e.g. todo, fixme, ...). Every one of them can be assigned custom colors/backgrounds in the editor. You can also define filters that limit what is shown in the todo dockable frame.

But you are right, there really seems no way to show some with a warning marker and others with an error marker.