A high degree of what? You must say. Also, "effects" and "problems" are too vague to measure so they don't really fit with the word "degree", which is quasi-quantitative. For instance, you could say "The rate of fossil fuel consumption justifies a high degree of alarm." "The effects of fossil fuel consumption are evident to such a degree that they can no longer be ignored." (The degree of evidence is strong.)

Instead of degree use 'level'.

In isolation, they aren’t very clear or natural. The problems from burning fossil fuels are serious. (Talking about a general relation with problems now but also in the future.) The problems from having burned fossil fuels are serious. (Talking about now. In some versions of English, ‘burnt’ might be preferred over ‘burned’) Though not wrong, you don’t need the present perfect because you are explicitly using words whose meaning connects the present or ongoing effects to past behavior.