I will take part in your survey :)
What is the way it is done in your favorite racing game?
I prefer when the car is slowed down or stopped and damage is applied to the car. After enough damage, the car's handling or top speed is reduced.
How is it done in other successful racing games?
I don't play a lot of racing games, but the ones I'm familiar with will cause a slow down + damage. Unless the accident is really bad, then the car will be destroyed on impact.
Do you think temporarily disabling the engine for a second is too
severe?
For a full second? Not if the car can maintain existing momentum. If the car had to stop for a second, then get back up to speed it may be a problem. You'd have to play test it and see what felt right.
If I do go that route, how would I convey the 'engine is disabled' to
the player in a subtle and easily understood way?
You could flash an engine icon at the top of the screen and/or play sounds of a sputtering engine. Or sounds of an engine revving up out of gear.
Is this 'too much' of a penalty?
You can change the time of the delay based on the severity of the impact. So players will know that a severe penalty was their own fault.
Would the slow-down from the collision be sufficient to discourage the
player from driving too carelessly?
I guess that depends on the player. If the slowdown was significant enough, they wouldn't drive carelessly any more. But if it's too much, they might not play anymore.
Which one is more fun?
Blowing up the car when it takes too much damage is typically rated 3 funs above just slowing the car down.
Should I consider a health-bar and affect engine performance for 'low
health' status?
Since you don't mention if the racing game is realistic or cartoony, I'll assume cartoony. Yes, have a health bar. The engine should slow down and make coughing noises when it's very damaged.
Could you offer examples of games that handle this well and one that
do it poorly?
I don't remember the specific names of the games, but I know there was one racing game where when you hit something and slowed down, the AI racers were always right behind you to overtake you. No matter how much of a lead you had on them. Don't do it that way.
Please share your experience with racing games obstacles and reference
games you feel perform well in this aspect.
Again, I don't remember the specific names. But there was one that would just slow you down and have realistic body damage to the vehicle when the car was hit.
I would also like to hear how you feel we should penalize or reward
for colliding with other vehicles?
Same deal, cars should be damaged based on the severity of the crash. For example a head on collision would be devastating, but a side swipe would be barely anything.
Should enemy vehicles be destroyable? Should they slow down severely
when they hit the back of your car or would that make the gameplay
imbalanced?
Yes! Take them out of the race. Enemy vehicles should have all the same penalties as your car. You should be able to side swipe them to make the crash into other cars or trees.