We are not quite sure how our affectivity (emotions, passions, and so on) will work in Heaven before the General Resurrection, however the Church teaches dogmatically that all human beings will receive their bodies at the General Judgment. As the Nicene-Constantopolitan Creed (the one said at Mass nearly every Sunday) says
I look forward to the resurrection of the dead and the life of the world to come.
See also the Catechism of the Catholic Church, nos. 992-1004 and 1038.
Being in Heaven, therefore, does not destroy our human nature—including the corporeal aspects of that human nature, which is necessary for there to be affectivity in the strict sense—but rather perfects it.
It follows that there will indeed be emotions and affection in Heaven—not exactly the same as on earth (for one thing, there is no marriage in Heaven—see Matthew 22:30 and the parallel passages), but more perfect and more intense.
UPDATE (because of expansion of question)
When the Church teaches that human beings will impassible in Heaven, it specifically means that we will be unable to suffer (i.e., experience pain). It does not mean that we will be incapable of experiencing passions (emotions, affections, and so on). Passions, understood in this latter sense, are part and parcel of human nature, and so they will not be destroyed by the Beatific Vision—indeed, they will be intensified. (See, for example, Catechism No. 1044.)
Of course, they will not be disordered, as they frequently are here on earth. Moreover, the conditions will be different, because the persons in Heaven will be before the very source of all their longings—namely, God. In Heaven, therefore, we will be in the condition of having all our longings—our very deepest longings—perfectly fulfilled.
(God, on the other hand, is impassible in every sense—not because He lacks love, but because His love is constantly active—as the O.P. points out. God cannot experience emotions in His Divine Nature, because one needs a body for that; however, since He is the Creator of the emotions, He experiences something even better than our emotions.)
In short, all of our faculties will be operating at their “maximum” in Heaven: through our will, we will love God (and our neighbor) intellectually; through our sensitive appetites, we will be drawn to Him, they will be actuated at their maximum intensity, and hence we experience affection for Him (and our neighbor).
In short, we will experience all the types of love that are characteristic of man—active and passive, intellectual and sensitive—but at their maximum intensity and without disorder.
Sources for more information
The best source for more information is the Summa theologiae of St. Thomas Aquinas.
Regarding the faculties of the soul—intellect, will, and sensitive appetites—have a look at I, qq. 79-82
Regarding the passions (Thomas’ term for emotions, feelings, and similar phenomena), the entire Ia-IIae (first part of the second part) is relevant; but especially qq. 22-25. Also interesting are the questions regarding the passion of love, qq. 26-28.
Regarding heavenly beatitude, see I, q .26, especially Article 4.
Also, see St. Thomas on the Christ’s glorified body (which applies also to our own body after the General Resurrection): III, q. 54, a. 3.