Do astronauts deploy parachute during reentry

If you're asking about the deployment of the three main parachutes of C/M-ELS (Apollo Command Module Earth Landing System), then this is simple enough to answer, the pilot chutes are deployed at about 10,000 feet (3.05 km) by a barometric switch, pulling the three main parachutes from their containers. The ELS was designed so the drogue chutes slow the descent down to roughly 200 km/h (124 mi/h) before the pilot chutes pull the main chutes, eventually slowing down the CM to 22 miles per hour (35 km/h) for splashdown and to roughly 24.5 mi/h (39.5 km/h) with only two main chutes properly deployed, as it happened during the Apollo 15 splashdown.


                  Earth Landing System sequence of events (Source: Project Apollo - NASSP)

For the drogue deployment though (thanks go to @MarkAdler in the comments!), we now have this diagram of the parachute deployment envelope:


So in normal atmospheric entry (not launch abort), the diagram for manual deployment of the drogues describes the region in altitudes between 40,000 and 25,000 feet (12.2 - 7.6 km) and CM velocity between mach 0.7 and 0.3. Translating that to US standard atmosphere in 1962 figures, 0.7 mach at 40,000 feet equals roughly 206 m/s (743 km/h or 461 mi/h) and 0.3 mach at 25,000 feet equals roughly 94 m/s (338 km/h or 210 mi/h). That averages out at 32,500 ft (9.9 km) and velocity of 150 m/s (540 km/h or 336 mi/h).

The normal entry region for drogue chute deployment by barometric switch (such as was the case with Apollo 11) is described at altitudes between 25,000 and 20,000 feet (7.6 - 6.1 km) and CM velocity between mach 0.225 and 0.475 that come out at roughly 70.65 - 147.25 m/s (158 - 329 mi/h or 254 - 530 km/h). That averages out at 22,500 feet and 109 m/s (243.5 mi/h or 392 km/h).