Does a pre existing diabetes diagnosis escalate the burn degree due to neuropathy, or should such patients just make visual inspection?

Not sure of question. Diabetes can cause peripheral neuropathy and make it easier to get injured without realizing it. Visual inspection of the feet is important, especially if they are numb or have reduced sensation.
Yes it may. Yes it may but clearly it depends on the extent of neuropathy and severity of the diabetes which may effect other aspects of response to injury and healing.
Yes and no. Diabetics with peripheral neuropathy may be prone to deeper burns because their sensibility is impaired. Also remember that full thickness burns (the most serious) typically are not painful because the nerve endings have been destroyed. If you are diabetic and have any concern about the seriousness of a burn, contact your regional burn center immediately to be evaluated.
Unclear on question. Do you mean "does dm increase burning sensation due to neuropathy"? If so, then it sometimes can. Neuropathy can either cause numbness, pain or paresthesias (weird sensations like burning, tingling, or walking on pebbles). If you mean "does dm neuropathy increase the risk of getting a burn", the answer is also yes especially if there is significant numbness. Daily foot inspections are necessary.
A pre existing. Diabetes diagnosis escalates the risk for infection and other complications due tons burn.