I have a Canon 700D body with a standard 18-55 IS STM lens. Would I notice any improvements in image quality if I switch from the kit lens to an EF-S 24 mm 2.8 prime? I also have a 50 mm 1.8 STM, and the difference in image quality when compared to a kit lens at 50 mm is very noticeable - would it be a similar improvement with an EF-S 24? I have a 55-250 IS STM telephoto to cover longer focal lengths.
Would I notice any improvements in image quality if I switch from the kit lens to an EF-S 24 mm 2.8 prime?
Judging by the test charts on the-digital-picture.com, sure. At 24mm, and identical aperture settings, the 24/2.8 STM has slightly better IQ performance to the 18-55@24mm up until f/8. At which point, they're pretty much the same. But what looks like a difference on a test chart may not mean much in practical terms.
Get the 24mm if you want a pancake f/2.8 lens over the 18-55 kit. But realize that it sucks at covering any focal length other than 24mm.
I know it seems like the 50/1.8 has better IQ than the 18-55, but if you try using them both around f/8-f/16 you probably won't notice much difference especially if you don't make large prints. And you'll also want to notice that the 50/1.8 gets considerably sharper in the f/2.8-f/4 range than it is wider than f/2.8. Fast lenses are at their weakest wide open, and will exhibit things slower lenses won't: vignetting, longitudinal chromatic aberration (purple fringe), etc.
There are good reasons to love primes over zooms, but zooms can keep you from having to cart four to five lenses around, and used correctly can perform quite well. Go google up images taken by your 18-55 kit lens around the web. The limiting factor on it can be your experience and knowledge as much as the glass in it. Chasing glass gets expensive and can lead you down some wrong paths if you don't master technique first.