I would welcome it if space icons would be displayed if there were any present.

There's some other stuff too in Linchpin where you can put icons, for example the Linchpin Teaser or Profile Header fields.

Would you expect to be able to put your own icons in any of these cases?

Would you be okay if in all these cases we used the same icon set (that would have to be larger than it is now to accomodate the different use cases) or would you prefer to have different preselects plus the custom option?

I'd like to hear some opinions about this :)

What he said! ^