Conclusions:
I. At least Some Nails are Hands.
II. At least Some Fingers are Legs. Statements:

From Statement I. Some Hands are Legs (I) + All Legs are Nails (A) → Some Hands are Nails (I) → Conversion → Some Nails are Hands (I). Hence conclusion I follows. Some Hands are Legs (I) → Conversion → Some Legs are Hands (I) + Some Hands are not Fingers (I) → No conclusion. Hence conclusion II does not follow. From Statement II.   All Hands are Legs (A) + All Legs are Nails (A) → All Hands are Nails (A) → Conversion → Some Nails are Hands (I). Hence conclusion I follows. Some Hands are Fingers (I) → Conversion → Some Finger are Hands (I) + All Hands are Legs (A) → Some Fingers are Legs (I). Hence conclusion II follows. From Statement III. All Nails are Fingers (A) → Conversion → Some Fingers are Nails (I). Some Legs are Fingers (I) + Some Fingers are Nails (I) → No conclusion. Hence conclusion I does not follow. Some Legs are Fingers (I) → Conversion → Some Finger are Legs (I). Hence conclusion II follows. From Statement IV. Some Nails are Fingers (I) + No Finger is a Leg (E) → Some Nails are not Fingers (O) + All Hands are Fingers (A) → No conclusion. Hence conclusion I does not follow. No Finger is a Leg (E) → Conversion → No Leg is an Finger (E). Hence conclusion II does not follow.