Should my pedal be this shape or is it bent?
Should my pedal be this shape or is it bent?

Yes, your pedal is bent.
I drew some straight lines on your photo to illustrate the places I see bends.

&quot;Side A&quot; is bowed in toward the pedal axle.
&quot;Side B&quot; - the ends are bent toward the crank arm.
In a more direct top down picture I think it would be clearer that your pedal is no longer a rectangle - a quadrilateral with four right angles - and that the whole pedal cage is off square.

can I bend them back?

Yes you can bend them back.
If you:

Figure out exactly what it should look like.
Analyze where you need to bend to get it back to ideal
Carefully apply force in the correct place

You can get it closer to the original but probably not perfect.

If they are in place on the outside cup the inside edge rolls round the nut of the axle. I wanted to replace the dust caps to stop them gunking up inside but it would cause them to sit in this position.

I'm not sure what this means - possibly that the cage is no longer connected to the axle housing preventing the installation of the dust cap. Straightening the cage may help, but it also might make it worse.
It might be best to ride what you have until you can afford to replace the pedals and not worry about the dust caps.
Maybe look for some used pedals in better condition.