With a modern parachute, how fast does it slow you down, and to what speed does it slow you down to? (so what’s the minimum deployment height?) how does this compare with the parachutes of say WWII era?
Bashere’s numbers are pretty good. 1000 feet per minute is a good ballpark descent rate for a modern ram-air canopy however since you’re flying an inflatable wing you can descend considerably faster by putting the canopy into a dive.
The time it takes the canopy to open can be altered depending on packing technique and so on but I’d say mine takes around 3 seconds or so to deploy.
The main canopy is packed with comfort in mind. Since the main is typically deployed at altitudes of around 2000-4000 feet (depending on the experience level of the skydiver) you don’t need it to snap open in a fraction of a second (overly fast deployments at terminal velocity can cause injuries).
The reserve canopy is built to open considerably faster for obvious reasons. Comfort isn’t really the concern, the aim is to have an open canopy overhead as quickly as possible with minimal risk of injury. I had to use my reserve once as a student (old round reserve) and it stopped me in about 1-2 seconds from terminal velocity (I had a high-speed total malfunction on the main). It wasn’t comfortable (my neck and shoulders were sore for a while afterwards) but I walked away from it.
Minimum deployment height will vary a lot depending on things like how fast you are falling. A modern automatic activation device (AAD, little gadget that students and many experienced skydivers carry) will attempt to deploy the reserve at about 750 feet above ground level if emergency conditions are detected (falling too fast at a low altitude). I’ve seen video of a cutaway from an open main and subsequent deployment of the reserve starting maybe 200-300 feet up (note that this is basically from a standing start, not falling 120mph). I’d say the reserve will certainly deploy in “a few hundred feet”, although skydivers are trained not to waste time once an emergency occurs. I’d much rather deploy my reserve at 2000 feet than 500 feet.
BASE jumpers (people who skydive from fixed objects) are another case altogether, because the altitudes are so low and the falling speed of the jumper is so slow the equipment is modified to open very quickly. I had friends who used to BASE jump and they would routinely do jumps from a few hundred feet, sometimes down to 100-200 feet. I would not recommend that myself 
If you’re asking about military parachutes, they vary depending on the jumper’s weight and air temp and density. But they keep your rate of decent around 18 ft per sec. The T-5s in WWII were a bit faster (18-22) than modern MC1-1Cs (14-18), but they all pretty much suck to land with.
Practice jumps in peace time are usually done at around 1250 ft. A true combat jump would be done at around 600ft or so.
The modern MIRPS reserve parachute will delpoy in about a second and a half and slow you to about 22fps.
Yep, my C2 vertebra (the Christopher Reeve one) was broken in half by an opening shock.
Ouch. Did that happen right around when Zero-P canopies and that really thin 550 spectra line all started showing up at once? I remember all kinds of packing advisories coming out from PD and other canopy manufacturers warning about line dump and some harsh openings.
Oh and one more tidbit for the OP - I saw video of a dual-canopy BASE rig (I think it was called the Sorceror) which showed a cutaway from the main canopy followed by complete deployment of the reserve canopy in something like 35 feet. A dual-canopy BASE rig is already unusual (most BASE jumpers only carry one canopy since there isn’t much time to go for Plan B in the event of an emergency) and this one had some work done to make reserve deployment as close to “instantaneous” as possible. It’s not really standard skydiving gear and those are definitely not standard conditions, but it falls in the same area as military zero airspeed/zero altitude ejection seats - they will get you down in one piece under same amazing circumstances.
The first flight of an advanced supersonic parachute system for Mars 2020—NASA’s next Mars rover. This video is narrated by Ian Clark, the test’s technical lead from NASA’s Jet Propulsion Laboratory in Pasadena, California. The test took place on Oct. 4, 2017, at NASA’s Wallops Flight Facility, Virginia. At the moment of full inflation, the parachute is going 1.8 times the speed of sound or nearly 1,300 miles an hour, and generating nearly 35,000 pounds of drag force—drag that would be necessary to help slow a payload down as it was entering the Martian atmosphere. This is the first of several tests in support of NASA’s Mars 2020 mission.