I agree with specialmom about the sebum. We all produce it.
The hard black pieces are commonly referred to as “blackheads”. Many of us get these, along with pimples when we’re younger. How old are you?
Keeping your face clean aka washing a couple of times/day can help keep the skin clear, but if you wash too often or with harsh soaps, you can make things worse by drying the skin too much. You might try washing with a medicated soap, then try using an astringent, applied with a cotton ball. You might also want to look for a non-greasy moisturizer since you don’t want your skin to get too dry.
You could also talk to your doctor or see a dermatologist.
Hi. I'm not exactly sure what you are talking about but it could be 'sebum'. We all produce this. It's like a waxy build up. It is on our skin but it can build up and make these plug like things. https://www.healthline.com/health/beauty-skin-care/sebum Cleaning your face regularly with products made for oily skin can help.