1. Your spider plants have fungus gnats. This is common in over watered houseplants, i.e. when the soil is never allowed to dry out.
Here's info about fungus gnats: https://extension.umd.edu/hgic/topics/fungus-gnats
Let the top inch of soil dry out between waterings. Do not let water sit for long periods in the saucer after you water. If this does not kill the gnat's larvae in the soil, then you may have to repot your plant with fresh clean soil.
2. This is bird's nest fungus, a harmless fungus that lives on dead organic material, which is what mulch is. No treatment needed. Here's more: https://extension.umd.edu/hgic/topics/mulch The link "What's Growing in my Landscape Mulch" is very good.