Lots of mistakes. Radars regularly track targets moving at mach 25, that's more than 8Km/s, 4.8Km/s is easy. How else do you think satellites are tracked? They are moving even faster at mach 28, more than 9Km/s. The S-400 can intercept targets up to 4.8Km/s, that's mach 14.
MIRV warheads fall due to gravity, it's nothing special. What's special about MIRVs is a missile can carry 3 or more warheads. Even missiles that have only one warhead come with reentry vehicles. During interception, the warhead is not changing directions, it is merely falling.
The S-400 was designed to intercept MIRVs. Along with other BMDs. For example, a battery can target 12 warheads. So a missile with 12 MIRV warheads can be intercepted by S-400. The only major criteria is the warheads should be doing less than mach 14. Since Delhi may have a minimum of 10 batteries, the S-400 can intercept 120 warheads at the same time. So you will need enough missiles that can carry 120 or more warheads to saturate the defences. This is not counting the Indian Phase 1 BMD.
If the Ababeel has 3 warheads, then Pak will need more than 40 missiles to saturate Delhi's S-400s. Of course, as time goes, the S-400 will be upgraded to be able to handle more threats at the same time. The Indian BMD is no different.
Missile speed depends on the range and altitude. So ICBMs have more speed, mach 17-25, SRBMs have the least speed, mach 2-3. So a missile fired from Pakistan towards Delhi is not going to be doing more than mach 10 even from the furthest ranges possible. Such missiles are significantly slower than 3Km/sec.
However, other cities in India are under greater threat of nukes. But for that there will be 2 new missiles introduced in the S-400 family that can stop targets up to 7Km/s. Plus, the phase 2 of the Indian BMD program will also be able to stop IRBMs. So any missile fired from inside Pakistan to any part of India will be stopped by the BMD. The Phase 2 BMD and the new missiles for the S-400 are primarily targeted to stop missiles that can be fired from any part of China into India.