BeccaT

this is absolutely brilliant, thanks so very much for your help! I can open the file fine :) 

OK, I opened the EPS, and it works the way I said: fold out the layer groups and click on one layer after another. You will then see what vectors doesn't show any information except that they are selected. Go to the brushes panel and choose one with a fitting thickness. Just click on it while the invisble vector is selected. So it should become visble. Do it with every invisible vector.
This will be a lot of work, but I don't know an easier way.
Edit: @Joachim_L: That's cool. As I opened the AI in Designer, it was just one layer with absolutely no content.

As Inkscape refuses to open the AI, I am pretty sure, that the PDF stream is missing. Another option would to convert the AI to PDF e.g. on https://convertio.co
I took your AI, converted and opened in AD and as far as I can tell it looks good. PDF is attached.
MERC0283(1).pdf

The AI is nothing spectacular. The EPS and PDF are showing nothing for me. I opened the AI in Illu, adapted the canvas to the outer bounds of the drawings and saved it again with PDF stream (perhaps this part was missing?) and it opens fine now in AD. Corrected file attached.
MERC0283-neu-kompress.ai

With "ESP", I think, You mean EPS (encapsulated postscript), right? My suggestion is, that those strokes that are visible on your second screenshot, are drawn in Illustrator with brushes that Designer doesn't support. But I'm not really sure. Anyway, the vector data of those strokes must be there, I think. So there must be layers with invisible content. If you test the single layers just by clicking on each after another, you should see that there are those vectors without strokes. In that case you should be able to give each vector a stroke. Not sure if this will work, but would be worth a try, I think.

What Old Bruce said - check to make sure your PDF reader is showing you the document outline, not the thumbnails.
For the sake of clarification, if anyone cares, thumbnails, the document outline, and bookmarks are all PDF navigation methods. Confusingly, document outline entries are sometimes called "bookmarks," but they are actually two different things.

You should see if your PDF viewer has the ability to show the ToC or Bookmarks. This sounds like it is set to show Thumbnails.

Hi Kahla,
 
You may want to copy the downloaded installation files to an external drive or USB stick. Once you have your new computer, you can copy the files across to then run the installations again. You will then just need to enter the email address and product key that you was supplied in your emails or by logging into your Affinity store account.

I think I understand it
I think that an approach like this should work, but I've never tried it for your purpose.
Find a set of images of the same object that match, except for the different attribute. Use File->New Stack, then select all those images. Specify Automatically Align Images. That should give you a new document, with all the images as layers, with the object aligned. Manually crop the document as you'd like it. Switch to the Export Persona. Using the Layers panel, create one slice per layer (image) to export. Export the slices as individual images.

Wonderful, thanks so much Dan!

Hi BeccaT
Please select all your Curve objects then go to Layer>Geometry>Merge Curves and try placing your image again. This action converts multiple 'Curve' objects into one 'Curves' object, as an image can only be clipped inside a singular layer, which is why you're only seeing the fill in one 'Curve' object. I hope this helps!

My guess is the obvious one: it is the embedded ICC profile data.
When I open the file on my Mac, it is set to use the "U.S. Web Coated (SWOP) V2" Color profile. In the resources of the Mac version of Affinity Designer is a file named "USWebCoatedSWOP.icc" & its file size is 557 KB. If I just change the document color profile to the "Generic CMYK Profile" the export size drops to about 90 KB at the 100% JPEG quality setting, which correlates well with the size of the built-in Mac OS System/Library/ColorSync/Profiles file of the same name, because its file size is 55 KB. 

Brilliant. This works for me too  
I keep having problems with file sizes so now I know what to look out for. Thanks so much for your help!

You're welcome.
So, here's something interesting. If you output your CMYK document as RGB instead of CMYK it's only 28KB. I'm not sure why a CMYK JPEG file is so much larger when Designer produces it.
I opened the CMYK JPEG file in IrfanView and resaved, and it dropped to about 15KB. Also, unchecking Embed ICC Profile during Export from Designer (on the More...) page drops it to about 33KB.
As exported from Designer, in CMYK, and with the ICC Profile included, exiftool shows a bunch of binary data that is missing from the version saved by IrfanView, but I have no idea what it is:

Please check if Menu View -> View Mode -> Outline is checked. If yes, change to Vector.

Thanks, Dan. You cleared that up for me very nicely.

Or you can download my file, good Alfred.
Best regards!
Spiral Template.afdesign

Hi Alex,
 
There's a couple of different ways... The easiest is just to select the object, go to the Gradient Fill Tool and choose 'Bitmap' from the drop down list shown in the context toolbar - choose a file and you're done. Other ways include inserting the image into the document, then using the layers page to drag the image to be a child of the circle/rectangle, or even just selecting the circle/rectangle then choosing 'Inside' from the target modes available at the top right of the application, then inserting a new image (which will automatically place it as a child of the circle/rectangle)
 
Hope that gets you going :)
Matt

Hi everyone,
 
I just wanted to let people know that I've put up a blog article explaining what layer blend modes are, how they are grouped together and what they do. I also give an visual example of the different blend modes so you can see the effect they have on your images. Here's the link - https://theeagerlearner.com/your-big-friendly-guide-to-layer-blend-modes/
 
Hope it's of help to you,
Simon

thank you so much  @John Rostron @haakoo @gdenby @v_kyr for the different options which are so helpful. For info, I used the vector with gradient fill, adding 0.1px  gaussian blur/alpha protected which achieved exactly the result I was looking for

thank you so much  @John Rostron @haakoo @gdenby @v_kyr for the different options which are so helpful. For info, I used the vector with gradient fill, adding 0.1px  gaussian blur/alpha protected which achieved exactly the result I was looking for

‘Rainbow’ is one of the styles supplied (along with ‘Sunset’, ‘Metal’, ‘Onyx’, ‘Glass’ and ‘Salmon’) in the Default category in the Styles panel in both AD and APh.

I think that what @BeccaT (the OP) has posted is a blow-up and that each block represents a single pixel. I cannot solve @BeccaT's problem, but this might help others do so.
John

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Note however that the above said is when using a vector shape with a rainbow style as fill. - If you instead rasterize the vector shape first, you can afterwards use the fill tool and apply directly another color onto the pixel.