The first reaction is acid/base, or more specifically decomposition of a carbonate by an acid. Carbonic acid H2CO3 is weak, so readily displaced by the much stronger acid HCl; it is also spontaneously unstable, decomposing to water and carbon dioxide, which escapes as gas:
CaCO3 + 2HCl -> CaCl2 + [H2CO3]
[H2CO3] -> H2O + CO2 (gas)
The second reaction is a 'double decomposition' which occurs when a solution contains ions any of which can combine to form a salt of low solubility. NaF and CaCl2 are both soluble in water, NaF giving Na+ and F- ions, and CaCl2 gives Ca2+ and F- ions. When the solutions are mixed, the Ca2+ and F- ions form insoluble CaF2 as a precipitate. The Na+ and Cl- ions remain in solution as sodium chloride is soluble in water.