Both of these questions relate to the driver and have nothing to do with Qimage but I'll see if I can help.  First, in order to print a 20x24 on a 24 inch wide roll, there are two options.  The first is to use borderless mode and set the paper size to 24 x 20.25 so the print will fit.  The second option is to set the media size to something like 24 x 25 and not use borderless: then Qimage will print the 20 inch side across the 24 inch width and it'll have room to print the 24 inch side along the length of the roll.  The key here is that you have to specify 24 inches as the width because that is your width (can't lie to the driver).  Then on the length, you need a little more length than the print because the printer has some leading/trailing non printable margins.

On the second question, that'd be a question to ask Breathing Color.  The media type dictates the ink that is used so if they created a new media type, they would have to be sure it uses the correct black ink.  If it isn't, the error is in the custom media type.

But other than the above, Qimage is just following the driver's lead.  All software has to.  Even when Qimage shows "Unlisted" as the media type, Qimage is correct: the newly added custom media type is not listed by the driver.  That's not really a problem: you can select it in the driver.  Qimage simply cannot display it because the new media type was not added to the list of media types supported by the driver.  That's the fault of the (Epson) software that installs custom media types: it adds the custom media type to the driver but the driver does not then report that new type to Windows as it should.  The only down side is that you can't select that media type directly from Qimage's Media Type parameter since Windows knows nothing about it; you have to select it in the driver instead and Qimage won't know the name because it is "unlisted" to Windows.

Regards,
Mike

The ICC profile has nothing to do with what ink is used (mattte or photo black), meaning: the ICC profile doesn't control the type of black ink that is used.  That is controlled by the media type setting.  Affinity Photo doesn't allow you to select media type outside of the driver like Qimage does: you have to go into the driver and select media type in there.  So you should be doing the same thing in Qimage: select the media type in the driver.  If Qimage then shows a media type of "Unlisted" on Qimage's Media Type setting, leave that alone: it just means the utility you used to install your new/custom media type didn't do it's job and add that media type to the list (to the Windows OS).  That means nothing, other than Qimage can't know the text name of the current media type so it tells you that the current media type that is selected through the driver has an "unlisted" name.  Which is fine...  it'll work fine but the name of the paper just wasn't reported to Windows, and therefore Qimage.

Mike