I like KhedrubGyatso's way of associating the EQ to the aggregate of feeling, the IQ to the aggregate of perception and the mental factors to the moral aggregate. It makes it easier to understand and relate to.
I find Hope Rainbow's questions to KG quite challenging. Unless we have some realisations, we can rely only on what is taught by Buddhist masters or from books on the subject matter.
I'll try to answer the questions with my limited knowledge of dharma.
Do we keep our aggregates when we die? According to Alistair Shearer (in "Buddha the Intelligent Heart"), "At the time of death, the grouping of mental formations that constitute what we call an individual mind leaves the disintegrating gross physical shell and moves to the subtler levels of creation. From here, at the time determined by its constituent elements, the bundle of mental tendencies will again return to the material plane as the seed-energy of whatever physical form is appropriate to the unfolding of its potential in the next incarnation."
Do we keep our consciousness when we die? Yes, the mind (consciousness) that leaves the body at death is the same mind that takes a new body in its next rebirth.
Do all aggregates dissolve to be recreated in another body? Maybe you mean the elements that dissolve. There are many books that describe the death process, for eg. Sogyal Rinpoche's "The Tibetan Book of Living and Dying". Aggregates do not dissolve, but they can be purified. Actually our liberation depends on our ability to purify and transcend them.
Is there a difference between mindstream and consciousness and feelings? I think mindstream and consciousness may be similar but consciousness and feelings are different aggregates although they are both mental. We can talk about our own mindstream and the need to purify it etc, but the mindstream or the mind of enlightened beings are already pure because they have no karma. I read somewhere that karma and mind are inseparable. As long as you have mind, you have karma. Once karma is exhausted, mind ends and becomes Dharmakaya, which is absence of karma. This mind is in fact none other than ultimate bodhicitta. So as long as we have mind, we have to take rebirth, as long as we have karma, we are trapped in samsara.
Is there a "dream-body"? I'm not sure what you mean. But I hope someone can explain what happens in the bardo. In Buddhism there is no concept of a "soul" entity. When one dies, one goes to the bardo as a formless being. This being may still have the mental aggregates but obviously not the physical one.
When one enters the womb, how do the aggregates form, do they form all at once or is consciousness arising late in the process? From my limited understanding, I think the consciousness is already there when the embryo forms. We carry with us from life to life the vicious circle of repeated patterns of thought, feeling and behaviour that keep us in samsara. So the aggregates are not formed in the body. Karma follows us like a shadow , remember?