Dark energy and dark matter: Roman will constrain the cause of cosmic acceleration by combining galaxy clustering and weak gravitational-lensing measurements with distances from Type Ia supernovae. Galaxy shapes reveal how foreground mass bends light, enabling maps of otherwise invisible dark matter; the expansion and structure-growth measurements together test whether dark energy behaves like a cosmological constant or whether gravity differs from general relativity on cosmic scales.
Exoplanets: Its Galactic Bulge Time-Domain Survey will monitor hundreds of millions of stars for gravitational microlensing—brief brightening when a foreground star and any planets pass nearly in front of a background star. This is sensitive to cold, wide-orbit planets and free-floating planets that transit-based surveys often miss. NASA’s current estimate is about 100,000 planets from the technique, so the claim of “up to 200,000” is not the current NASA figure.
Direct imaging: Roman’s Coronagraph Instrument is primarily a technology demonstration. It will suppress starlight to enable direct imaging and spectroscopy of selected giant exoplanets and circumstellar/planet-forming disks, developing techniques important for future missions aimed at potentially habitable worlds.
Operations and readiness: Roman’s nominal mission is five years, with a 10-year goal. It has been loaded with 290 gallons—about 1,100 liters—of hydrazine at Kennedy Space Center, a major launch-processing milestone.
Relationship to Webb: Roman and JWST are complementary, not competitors. Roman is optimized to discover and characterize large populations and wide fields in near-infrared light; Webb is optimized for much deeper, more detailed observations of selected objects. Roman can therefore identify rare or statistically important targets for Webb follow-up.
Some headline figures in the question need qualification: NASA’s official material supports a field of view of at least 100 times Hubble’s and a launch advance of eight months, while the current NASA exoplanet estimate is around 100,000 microlensing detections. I found insufficient high-authority support in the available sources for the precise “500 terabytes annually” and “one month versus Hubble’s century” claims.