Piston engines (running leaded high-octane fuel) in general are common in small aircraft. Radials do exist, but most, I think, are inline engines (usually opposed).
Nonsense. There are hundreds of DC-3s still flying with 1200hp Twin Wasp radials. Service life of aviation engines is essentially infinite - they just keep rebuilding ‘em.
The Russian ASH-62 is still in production, and depending on spec can produce as much as 1100hp.
No, it isn't. The "new" 62 are just old stock, or made from old stock parts, or rebuilt frankenstein engines with some new parts, or are Dongan HS-5 restamped as original 62 to pass the type test.
I used to be an aviation fan in my childhood. Tried to build a motoglider, but the process stalled before I moved out of the country.
The Russian ASH-62 is still in production, and depending on spec can produce as much as 1100hp.