Castilian's suggestion makes sense-- in any case, Gijon to Avilés has got an awful lot of roadwalking through industrial suburbs, especially the 10km into Avilés, so unless your confessor has set this stretch as a penance, you won't lose much by starting out of Avilés.
In Avilés, credenciales are available at the Pedro Solis albergue on Gutiérrez Herrero, 1--- Gronze.com does not say if they can be had at either albergue in Gijon. In any case, they are usually available at the turismo (in Gijon the turismo is on the pier leading of Calle Rodriguez San Pedro and in Avilés at Calle de Ruiz Gómez, 21-- I dealt with the turismo staff in Avilés and they were very helpful, giving me a city map with the Camino out of town marked on it).
I can't answer your other questions as I did not stay in albergues along this route-- generally they have mattresses so you would not need a sleeping mat, but others might have better information. As far as footwear is concerned, I need boots--- you may not!-- but the trail was largely either on gravelled footpaths, or gravelled or paved country roads.