knee walls should be insulated. If, from the other side, you can see the plasterboard and the wooden studs, you can put fibreglass loft insulation between the studs, then roll another layer along to cover that.
you can probably find a depth near enough to the depth of the wooden studs.
I prefer mineral wool inside a house, rather that foamed plastic slabs, because it is incombustible and does not emit fumes in a fire.
I only use the brown stuff, treated with Ecose, which does not shed irritant dust and fibres. It is made by Knauf but also sold as an own-brand, the packaging will have the "Ecose" flash on it.
At this time of year the sheds will be trying to shift their stock cheap. Nobody buys heaters or insulation in summer.
There is a kind of fixing nail with a big disk on the head. Some people hold it in place with netting. this might possibly do but I haven't tried. You can also clad the wall with plasterboard if you want. It is easy to cut and nail in place, and quite cheap.
If you can find any gaps or cracks around walls or floors, seal them with expanding foam. i use the pink fire grade which expands and resists flame. It is marginally dearer than the pink. you can get a Fischer applicator gun, and the gun-grade foam cartridges, from builders merchants or ebay. You will need just one canister of gun-cleaner solvent.
As Monsignor Chauvet would agree, there is a lot of wood in a roof, so any opportunity to use fire-resistant materials should be taken.