Conclusions:
I. No Consumption is a Usage.
II. Some Consumers are not Consumptions. Statements:

From Statement I. No Usage is a Producer (E) + Some Producer are Consumers (I) → Some Consumers are not Usages (O*) + Some Consumers are Consumptions (I) → No conclusion. Hence conclusion I does not follow. Some Consumers are Consumptions (I) → Conversion → Some Consumptions are Consumers (I) → Probable conclusion → Some Consumers are Consumptions (O). Hence conclusion II follows. From Statement II. Only Producer are Usages → All Usages are Producer and Usages can have negative relation with anyone. Hence conclusion I follows. Only a few Consumers are Consumptions → Some Consumers are not Consumptions (O). Hence conclusion II follows.   From Statement III. All Usages are Consumers (A) + No Consumer is a Producer (E) → No Usage is a Producer (E) + Some Producer are Consumptions (I) → Some Consumptions are nor Usages (O*). Hence conclusion I does not follow. No Consumer is a Producer (E) + Some Producer are Consumptions (I) → Some Consumptions are not Consumers (O*). Hence conclusion II does not follow. From Statement IV. No Consumption is a Consumer (E) + A few Consumers are Usages (I) → Some Usages are not Consumptions (O*). Hence conclusion I does not follow. No Consumption is a Consumer (E) → Conversion → Some Consumers are not Consumptions (O). Hence conclusion II follows.