A - Another great question! This is fun answering all of these wonderful questions.
To give you a good answer, we will have to do a quick study in christology (theology on Christ) and fundamental theology on the Trinity. I love theology, so now you have gotten me excited.
As you have no doubt heard, there is only one God in three persons, but what exactly does that mean? It means several things. But, before I try to answer it, remember that we are talking about the infinite and were are finite. We cannot fully get our arms (or minds) around God. So, if your brain hurts while thinking/meditating on God, that is a good thing.
God is one.
God is three persons.
The three persons can never act one without the other two. This is because the three are always one. They differ, not in how they act, but in relationship to one another.
Now, this might sound contradictory, but it isn't. While we may talk about the Father creating, the Son redeeming, and the Spirit sanctifying, in reality all three persons do all three divine acts. When we refer to any one trinitarian person acting alone, it is with the understanding that the other two are really acting as well. This is called appropriation. We do it with traits of God as well (e.g., beauty in the Son, happiness of the Spirit, etc.).
God is unity. God cannot act with part of his being and without another. But, it is right and proper to talk about the three persons acting in this way, because the Bible tells us this is how we are to do so.
So, to answer your question. Do we receive the Father and the Spirit along with the Son in the Eucharist? Certainly we can say this is so, but must be careful. We do not receive the Father and Spirit as "body, blood, soul", but rather in "divinity". Whenever we receive the Son, we receive Father and Spirit as well. If you pay close attention, every Eucharistic prayer is trinitarian, including the epiclesis, where the priest asks the Holy Spirit to come down and transform the bread and wine.
John Paul II says:
In the Eucharist Christ gives us his body and blood as food and drink, under the appearance of bread and wine, just as during the paschal meal at the Last Supper. Only through the Spirit, the giver of life, can the Eucharistic food and drink produce in us "communion," that is to say, the salvific union with Christ crucified and glorified. (general audience Sept 13, 1989)The Catechism has a wonderful section about the trinity and the Eucharist in 1077-1112 and 1356-1361. I will put a few paragraphs that stand out here:
1357 We carry out this command of the Lord by celebrating the memorial of his sacrifice. In so doing, we offer to the Father what he has himself given us: the gifts of his creation, bread and wine which, by the power of the Holy Spirit and by the words of Christ, have become the body and blood of Christ. Christ is thus really and mysteriously made present.