These spots seem like typical dust spots. I encounter them regularly and are usually quite easy to remove in Lightroom or Photoshop. In the darkroom, it is more of a hassle. After meticulous dust removal pre-exposure, dust may still show (significant) spots on the print. Here, retouch kits are used.

You won't ever get rid of dust. You worded it nicely, it's a true plague. Depending on how the film was handled and stored, you'll get more or less dust, and the distribution can also vary between frames. There are however a few methods of reducing the amount of dust in your scans and prints:

1. If you develop film yourself, let the film dry in usually humid area such as the bathroom. The humid air catches a lot of the dust that's floating freely in the air and lets it settle on the ground, so it won't fall on your film.
2. Use pressurised air canisters to blow the dust from the film strips and scanner glass. Alternatively, you can use hand-powered dust blowers.
3. Use microfiber cloths to wipe the strips and glass clean. Static free cloths are a good option. I know Ilford uses or used to sell them.

If you are unsure whether you are dealing with dust or other artefacts, it is always useful to resort back to the negatives or positives. Check these for spots, this may help you in figuring out what is causing the artefacts you are seeing.

EDIT

The streaking you are referring to seems like slight bromide drag. Bromide drag can happen when the bromide in the film emulsion overpowers the developing agent. Solutions: either properly invert the tank when developing (so don't use the rotating stick), or use a stronger developer solution.