The render-thread is meant to create an image, of the images you put inthere like i've done :-) As for that, i'm pretty sure it's right :-D
It's definitely not. You're supposed to create the Image once when you load it and then pass out references to that Image to everything that needs it. At the moment, you're creating one image per player every frame. On top of that, you're not deleting your Image objects once it's no longer used. Although Java rarely requires you to manually unload/delete resources, Slick2D uses OpenGL which stores textures (= images) on the graphics cards video RAM, so it does require you to manually signal when to delete a texture.
Concerning your main problem, I'm pretty sure you're creating more and more objects each frame, most likely when you get network update or something like that. The "blurry" text is just the same text drawn with blending over itself lots of times, so the color approaches 1.0 for all pixels in the font that aren't completely transparent. You probably have lots of player objects too. You seem to have some pretty heavy memory leaks, so try to take care of those and the problem should fix itself.