@henriko You can get a new capacitor for the mixer at https://fi.farnell.com/kemet/f863bc104k310zv047/suppression-cap-0-1uf-class-x2/dp/4241936 . I would order 10 (you cannot order any less). They charge €15 for delivery.
These capacitors filter the electrical noise produced by the mixer so that the power in your house is not noisy while this is in use. The capacitor I linked is rated to handle temperatures up to 125°C, so it shouldn't fail due to heat, and if it fails, it fails safely. When soldering the new capacitor in, make sure to cover the capacitor legs with heat shrink or similar so they don't short out on the metal parts of the mixer.
I don't think there's a problem with the motor, but it's hard to know unless we replace this capacitor.