How fast does the ISS travel in m/s?

The figure refers to orbital velocity relative to Earth's center, not to a speed through air. At about 400 kilometers altitude there's no longer any appreciable airflow; the station moves at around 28,000 kilometers per hour, that is, about 7.7 kilometers or 7,700 meters per second, and takes about 90 minutes to complete one orbit. Anyone on board notices none of this: with no reference points or acceleration, the flight feels like standing still, and it only becomes visible when watching Earth pass below.

In a circular orbit, gravitational pull and inertia are balanced, and that balance is what sets the speed: the lower the orbit, the faster a body must move. Braking, therefore, doesn't mean stopping, but descending; speeding up raises the orbit, which makes a vehicle slower and leaves it lagging behind. This is precisely what approach maneuvers are based on, in which a cargo vessel doesn't simply arrive from behind, but catches up to the station from a lower, and therefore faster, orbit.

At these speeds, any particle becomes a projectile: fragments of space debris and micrometeorites strike with a force against which a rifle bullet is harmless, which is why crewed modules carry staggered layers of protection and evasive maneuvers are performed. The residual atmosphere constantly slows the station, so its orbit must periodically be raised with engines. And on return, that same kinetic energy has to disappear, which makes a capsule's heat shield the most critical component of the flight.