1. Yes absolutely 2. Madeira is denser and easier to decorate than sponge - it depends on how elaborate your decoration will be! 3. Wrap in silver foil before decorating and after decorating a cardboard cake box ideal otherwise a Tupperware style one 4. I have only used buttercream before using using fondant but sure I've read somewhere jam can be used.
I would think sponge would be ok as its small and not elaborate!
You're right about a plastic box possibly making the cake 'sweat' a bit, but if you haven't got anything else, it will be fine. I wouldn't use the lid - just use clingfilm or foil to lightly cover the top of the box. Fondant covered cakes keep quite well!
There seems to be a lot of obsession on MN for cakes to be Maderia. Maderia is suitable for carved cakes but a simple party cake can be anything really. Coconut, rich chocolate, vanilla, orange endless really but not a Victoria as this can be hard to cut - eg
butter cream, seedless rasberry or apricot jam all stick fondant to sponge.
If using white fondant with bright coloured shapes stuck or piped on it, leave white to dry as long as possible then add shapes with the tiniest drop of water (gin or vodca is even better because excess evaporates). Then the colours don't bleed even in a plastic box.
If you want to put fondant shapes, letters or figures on to a butter cream coated cake it's best to let them dry sat on a plate and put them on at the very last minute as they take up moisture from the butter cream.
Good luck and have fun, DCs appreciate anything colourful, especially if you let them have an input into the design. They don't care if it's perfect.
DCs also tend to like sweets, you can go a long way with smarties, chocolate buttons and interesting pick and mix and no skill at all.