WebUVs runs in your browser and needs JavaScript and WebGL turned on. If either is off, the page says so at the bottom. A browser that's out of date may lack WebGL too.
A message says why. The file may be damaged, or not the format its name says: an OBJ must be text, a .3ds or .i3d 3D Studio's chunks. See Opening files.
A material whose texture isn't loaded shows a stand-in on the model, naming the file it wants. Open that image, or drop it onto the texture box at the right of the material's row, in the Textures section. An image goes by itself to the material that names its file name, in the MTL or the model; one no material names goes to the active material, the one last clicked in the Textures section or that the selection is on.
The message names the object in the way. A mesh that takes part in a morph can't gain vertices, so new seams on it can't be saved; moving its UVs alone can. And a mesh holds at most 65,535 vertices and UVs. See Saving and exporting.
Your work is kept in the browser you used, and only there. It's gone if you opened another model, cleared the site's data, or worked in a private window. Another browser or device never had it.
A big model, or a computer without a graphics card, can make the 3D View slow. Hide the 3D View while working in the UV Layout, or show fewer parts at once from the Objects list.
Press Esc, or click Relax again, to leave Relax mode.