There are a lot of capabilities implemented in the Cycles renderer (global illumination, reflections, transmissive/refractive glass) that do not get bundled into the exported model. Eevee is closer to the behavior of realtime viewers than Cycles. Moreover a lot of materials in Blender cannot be exported to any format. If you’re planning to export a model to other software, you’ll want to familiarize yourself with the exporter documentation here:
Notably, any ‘lit’ materials should use the Principled BSDF material, and bake any complex node graphs down to simple texture or numeric inputs on each socket. Addons like SimpleBake can help with that. If you’re interested in the same lighting, you may want to bake Ambient Occlusion to a texture. The mirror is not going to reflect the rest of the scene in any realtime viewer I’m aware of, that is something that is easy for a pathtracer like Cycles but not so much on a realtime renderer.
For the glass on the shower you would use the “Transmission” option of Principled BSDF, or perhaps Alpha Blend mode. I’m not sure which viewer you’re using above, but perhaps try a few online viewers to make compare: