A lipids profile will be affected by consuming a greasy meal so if you have a questionable cholesterol level then you would be better to fast. In real terms a lipid profile is only valid if you fast for 8-12 hours. However generally a cholesterol result will be consistent regardless. My warning is if you have a high cholesterol avoid eating before the test.
A finger prick Haemoglobin will not be affected AT ALL by eating a meal. Hb will only change suddenly if you have acute blood loss (unlikely!)