Chop up the larger branches into smaller pieces and mix with compost and you have a bark like mulch. There are loads of shade loving plants that will like that - Spotted Laurel is attractive (variated Aucuba Japonica), Fatsia Japonica, Mahonia, Japanese Skimmia, Cotoneaster, Eunonymus and Camelia come to mind.

Primrose, Daffodils, Helleborus and Hostas will add colour.

No, Tropaeolum (nasturtium) won't like shade at all, they like a good baking in the sun.
Epimediums on the other hand would love it there and there are some beautiful pink and purple shades aswell as the common yellow/amber shades.

For shrubs, the previous person has given a good selection.

Whatever you plant make sure its resistant to slugs & snails as the environment you describe seems right up their street