Temperature-stable spices
Are there any systematical studies available?

I am not aware of any such study or resource, but ignorance of or lack of evidence of a thing doesn't necessarily mean that it doesn't exist.  

Which spices can easily bear long durations of broiling, hot oven or barbecue?

Broiling is an especially intense cooking method, directly transferring energy to the surface of the target food by radiation.  It also is not a method used for long cooking duration, because it is so rapid, and easily would burn or char the outside of the food.

As a general principle, hard, woody spices and hard seeds tend to be the most heat insensitive:  black pepper, cinnamon, anise, nutmeg, cumin and so on.

In the herb family, the hardier herbs (bay leaf, oregano, and sage for example) can stand up to some prolonged cooking without adversely affecting their flavor.

Delicate herbs (cilantro, parsley, tarragon, basil for example) do not fare well as their flavors are very volatile.

Which lose flavor or deteriorate quickly?

See above; this is just a rephrasing of the same question.

Which develop displeasing flavors?

This is an open ended list question.

For a significant portion of the population, cilantro starts with a displeasing flavor.

Badly overcooked garlic can become bitter, if you consider it a spice.  Similarly, paprika and many of the capsicum peppers become very unpleasantly bitter when burned.

Most flavors simply lose their intensity and become muted or difficult to perceive.

Which become unhealthy or even poisonous?

I am not aware of any.

What can be done to preserve sensitive spices during hot cooking?

Don't add them during prolonged cooking; add them at near the end of the cooking period or even after cooking is completed.