Wood ash is quite important to me with a wood burning stove, fair bit of phosphorus, mostly it gets mixed into compost.
Compost varies, depending what goes in to it, it can be quite low in nutrients.
Seaweed extract is low in N, but contains nutrients which are important in small quantities (Boron?) and calcium, magnesium, phosphorus, sodium, potassium, and sulphur.
If I can get them I mix horse manure and poultry droppings into my compost, they act as an accelerant, which means it gets hot and weed seeds are killed, and poultry manure is a bit dangerous straight.
I run two composts, a black bin on wire mesh to stop rodents getting in for kitchen waste, and an ordinary, open compost heap for general garden waste.
I bag leaves in Autumn for leaf mould.