Question: When we make offerings such as fruits to departed ones, can they receive them?
Answer: Only if they are hungry ghosts or wandering spirits, can they be received via the power of dedication, and to various extents, depending on their karma.
Question: How can we further ensure offerings will be received?
Answer: What we can do is to offer to the Buddhas and Bodhisattvas (or the Triple Gem on the whole) at the same time in the name of the departed, which creates more merits, which can then be dedicated to the deceased, wherever they are, to be able to receive the offerings.
Question: Why can’t beings in other realms receive them?
Answer: Beings of the hell realm have negative karma that is too strong to be able to receive the offerings, while beings of the heavenly realm have positive karma that is too strong to require such offerings. Unless the ones the food is dedicated to have been reborn as animals or humans who have access to the offerings, they cannot be partaken.
Question: When we offer the same to Buddhas and Bodhisattvas, will they receive them?
Answer: As they do not need them, they thus do not partake of them. However, they will know our sincere intentions of paying respect. In this way, when we cultivate reverence and generate generosity, we can create merits. Offerings have Dharma significance too (see page 167 of http://tinyurl.com/bealamp6). In this sense, the offerings are actually offerings of the Dharma to ourselves as reminders when we make them too. For example, the offering of fruits represents mindfulness of the law of karmic cause and effect, to diligently avoid all evil and to do all good.