(1) Background: The work presents results of concentration measurements of PM1, collected in the indoor air of four preschool buildings in Gliwice and its environs (Silesia Province) and in ambient air in the vicinity of four working hard coal power plants and four coking plants located in southern Poland. (2) Methods: The samples of <1 µm, 1–2.5 µm, 2.5–10 µm, and >10 µm fractions were collected with the use of Dekati® PM10 cascade impactor, and concentrations of seven trace elements (Cd, Cr, Mn, Ni, Pb, Sb, and Se) were determined. (3) Results: The concentrations of PM1 changed in the range of 3.1 μg/m3–65.3 μg/m3. Among trace elements, the highest concentrations in indoor air were evidenced for Cr (129–219 ng/m3), while in outdoor air for Pb (12.6–21.2 ng/m3). Principal Component Analysis PCA analysis extracted three factors of rural dusts, city dusts, and natural soils. (4) Conclusions: The paper points to accumulation of carcinogenic Cd, Cr, and Ni in indoor air, and significant contribution of trace elements in PM1, which, owing to long-lasting exposure and elevated sensitivity of developing organisms, may evoke effects on health of children.