Question: After offering fruits and other kinds of food at a Buddhist shrine in a temple or at home, is it alright to consume them?
Answer: Yes, they are alright for consumption. Some believe such food will be somewhat blessed as the virtues of reverence, devotion, mindfulness and generosity to the Triple Gem were expressed through them. Note that although the enlightened who are also fully liberated do not really need any food offerings, making of offerings is still a good practice for nurturing the above virtues, which also creates merits. The offering of fruits also remind us of to aspire for the fruit of Buddhahood, and of the law of karma (cause and effect), to remind us to avoid evil and do good (as within fruits are seeds of potential for further fruits).
Question: What about food offerings after a Dharma (chanting) ceremony, that were offered to the deceased?
Answer: Some believe food offered to spirit beings lose their nutrition if their essence was already consumed, claiming that such food might be bad for health, although others believe such food is totally alright to consume. There has been no proper study done to survey the consumers on the effects of consumption, while there are not many obvious ill effects that we hear of.
Question: How should such food be handled if I do not wish to waste it, while wanting peace of mind for consumption?
Answer: A recommedation is to put the food near a Buddha shrine for a while first, with sincere prayers to the Buddha to help bless or ‘recharge’ the food, to make it fit for human consumption, if it is no longer so. However, these foods should not be offered on the shrine itself, as they have been offered to spirit beings and in part consumed already, which makes it kind of disrespectful if re-offered.