I have tried all the chase missions and GTA 5, and got these results.

Don't mind the cutscenes, those are something else.

  1. Franklin and Lamar - Pretty easy. If you go fast enough or use Frank's ability, you'll be able to hit lamar's car, but he won't lose control as always known for these kind of chase scenes.
  2. Father and Son - Only the truck is fixed to the path. The trailer can sometimes be rammed in different directions.
  3. Chop - could possibly do it with frank's ability or fully upgrading the van using money mods.
  4. Three in a row. Marriage Counseling - Still trying. Probably not possible since you're driving as michael.
  5. The Jewel Heist (Both ways) - The bikes are fixed to path. I'll try this again sometime.
  6. Mr. Phillips - during the chase, the Gang Burrito is fixed to the path but can be destroyed. You don't see any marks coming from it's tires.
  7. Fame or Shame - Lazlow's car is fixed to path during the chase. I tried this once and managed to hit him by cutting through a turn.
  8. Hood Safari - During the shootout, all the cars pulling the spinout effect are fixed to their path, and then become free movable after the guys get out of their car, but can be destroyed while they're moving. The Oracle XS during the Seadoo chase though, is fixed to path but can be destroyed.
  9. Blitz Play- The police cars stopping behave the same way as those in Hood Safari.
  10. I fought the law - Once the race starts, the 2 supercars are fixed to their paths, until one point where near the time where the player shifts to michael, the Cheetah stops speeding and becomes a civilian vehicle, meaning you can ram him off the road, but not destroy it. During the regular race without the police on your ass, the cars can be easily passed and hit by using Frank's ability. Once shifting to Michael though, the Cheetah joins back in the race. Trevor is also fixed to his path during the Police chase.
  11. Eye in the sky - the Z type and Frank are fixed to their paths, despite not being able to drive.
  12. Predator - Can be rammed easily before going off the road while you're still on the highway - though nothing happens. Monk already said that the Dubsta cannot be destroyed either.
  13. The Paleto Score - I don't really remember anything.
  14. Bury the Hatchet - When michael leaves his house, Trevor as we knew, takes michael's car and then eventually disappears after.
  15. Legal Trouble - Cutting across a couple directions can lead you to ramming Molly easily. Some of the police cars can also be hit but also don't do anything. Molly could be possibly immune to explosions if used sticky bombs.
  16. The Big Score (Subtle) We know this, all 3 Gauntlets excluding Frank's are fixed to the path, same going with Karim stopping and getting arrested, But once he gets out, his Gauntlet can be rammed.
  17. Something Sensible (Ending A, kill Trevor) - This is pretty interesting. I was able to race him back to the oil fields without letting him pass me thanks to Frank's ability, he can be easily hit and gotten ahead of.
  18. The Time's Come - Tried this 2 times. At the very first try, make sure you fully upgrade Frankie's Buffalo as you'll need that to do this. Michael's car can be hit before making a turn onto the train tracks. Note that this can only be done at the first try, so if you fail at the first try, you'll not be able to do this again.
  19. Paparazzo - The Meltdown - I could tell that both Poppy and the Police Car were fixed to path by trying this on Old gen.

           -ZSS 3:27 PM, August 18th, 2016 (North America)