As has been noted, the GPS Signal includes satellite health information.
It is not true that Ionospheric correction is solely the domain of dual frequency or DGPS positioning. The ionospheric delays can be estimated by ionosphere modelling. This ionosphere information is included in the Navigation message and allows an independent (non-DGPS) single frequency receiver to apply ionosphere delay corrections to the received signals.
There actually are 2 time corrections encoded in the GPS signal. The clocks in the GPS satellites are very accurate, but not perfect. (cesium and rubidium atomic clocks, IIRC) The errors are small but significant for precise applications. When your measuring stick is traveling at the speed of light, a very small timing error translates to a fairly large distance error. So the GPS signal includes clock correction data for each satellite. And because the GPS system operates in its own time system, which is independent of UTC, the signal includes an offset for GPS time to UTC time. This offset is not constant, as GPS time is a stable atomic based time system, and UTC, while also an atomic time system, is adjusted periodically with leap seconds to keep it close to astronomic time based on the earth's rotation.