Hello,  I do not see a way to select a range of iterms in the transfers screen after completion.
Is there perhaps a hot key to simply start at top and press a key to delete -- and go to the next and so on?

You can use the same shortcuts that are available in windows explorer, as far as I'm aware.

You can use Ctrl+A to select all transfers. You can select a transfer, hold shift, select another transfer, and all of the transfers between the two transfers will be selected. You can also use Ctrl to select multiple transfers one by one.