Did the Russians ever come close to shooting SR-71 Blackbird

During the cold war the Russians tried many times to intercept SR-71 using Mig25. Did they ever come close to shooting it down?

If SR-71 was operational today, would it be able to fly over Russian with impunity?

Do the Russians now have any combination of aircraft and AAMs to challenge SR-71? What about Mig31 with long range radar and BVR missile?