Plant right through the mulch, cutting small holes where needed. Fertilizer is a material which provides nutrients to plant roots in a form that the roots can use. It is usually lower in percent of nutrients. It also adds humus to the soil. A chemical fertilizer is a manufactured product, compounded of various nutrients in a base material which allows spreading.
Plant roots use a chemical compound in solution which is taken up from the soil particles.
N, P and K are required most heavily and used up more quickly. Other nutrients needed are usually present in soil. Or use compost made up of several different materials. It's better NOT to apply fertilizer than to add too much. Too much fertilizer can kill plants.