Will my 15.6" laptop fit into this bag?

Yes absolutely....thats exactly what it was purchased for by my son.

Would this be able to fit a rugby kit and pe kit with folders?

Dimensions When Full: 6.3"W x 20.1"H x 12.6"L Volume: 1,769.7 Cubic In. / 29 L

Will it fit size 13 shoes?

I think though would struggle, I think size 11 max, you may be better off with a separate boot bag for size 13. My son's boots are size 7 and they fit nicely with a little bit of extra room

Will this bag be too big for an 11 year old boy starting secondary school?

Hello, thank you for your question and your interest in our product. The backpack has the following dimensions: 16 cm x 51 cm x 32 cm and has a volume of 29 litres. It therefore depends on the height of the child. If you're worried about compartments and the sufficiency, then yes there's plenty of storage and room for a 15 inch laptop or for books and an under compartment for shoes. If you have any further questions, please reach out to us again. Kind Regards, Your Under Armour Team