At what levels of muscle energy intake does catabolism start?
1) Yes, most cells in the body derive energy from oxidative metabolism, unless oxygen is not available for some reason. There are some exceptions, for example red blood cells lack mitochondria and so have no respiration, and various types of rapidly proliferating cells such as activated immune cells have high glycolysis and lactate production (for reasons that are still not well understood).

2) The main fuel of exercising muscle is glycogen, which can account for 60-80% of energy requirements (article). Triacyglycerols (fat) stored in muscle tissue may account for most of the remainder (artice). Normally, muscle protein is not a major energy source during exercise. Some muscle protein breakdown has been observed after 2-3 hours of intense exercise (think marathon runners), when glycogen stores are depleted. See this review article.

If glycogen is not synthesized and stored normally while resting, then muscle may be more likely to catabolize protein during intense exercise. This can happen to some extent in diabetes, see for example this paper. There are also severe genetic disorders that disrupt glycogen synthesis, but those are very rare. I would guess fasting also makes it difficult to replenish muscle glycogen stores (and muscle triglycerides as well), so strenuous exercise combined with fasting might result in muscle protein breakdown, but I don't know of a study on this.