So there are a lot of parts to this question, which touches on some pretty complicated parts of Greek history. So I am going to start by doing a bit of chronological definition: Greek colonization in a sense lasted up until the Roman period, and arguably longer. In the wake of Alexander's conquests, for example, many new cities (most famously Alexandria) were established and peopled with Greek transplants. But when discussing Greek colonization, we generally speak of the Archaic period, from roughly 800-500 BCE, or in other terms, from Homer to Marathon.

That out of the way, there are quite a large number of reasons for colonization, perhaps as many as there were colonies. The simplest was basic economic hardship. The Archaic period saw a steady expansion of the population of Greece as well as a simultaneous increasing concentration of wealth and power into the hands of the elite. The conditions for many people thus grew steadily worse, exemplified by the new institution of debt bondage, and colonization can be seen to have acted to relieve this pressure. As a rule I don't tend to favor "population pressure" explanations, but it was in the background. But not, of course, as the only reason. For example, the Phocaean colony of Elea/Velia was supposedly founded by refugees fleeing from the Persian conquest of their homeland. Others may have crossed the sea in search of fortune, or as a result of losing political struggles at home: the explanations were as vared as for modern immigration.

As for the links between colony and colonizer, it also varied. To give two examples from the Peloponnesian wars: the war actually began when the city of Corinth quarreled with its colony, Korkyra/Corfu, over the Korkyran colony of Epidamnus. So they could certainly be apathetic or antagonistic. On the other hand, when Athens invaded Sicily, Syracuse was able to call on Sparta for aid because it was a colony of Corinth, one of Sparta's allies. So there was definitely an awareness of their heritage among the colonists and ties persisted, but what that meant in political terms could vary a good bit.

As for native/colonizer relations that, as you may have guessed, varied. In Sicily the relationship seems to have been rather contentious--Athens' strategy during the invasion was to rile up the natives against the Dorian cities along the coast. In other areas, such as the Phocaean city of Marseilles/Massilia, the relationship was quite good. It really just depended.

There is a ton of work on this from different angles, such as Jonathon Hall's Hellenicity about the growth of Greek identity or the economic perspective in Justin Walsh's Consumerism in the Ancient World. Honestly the best bet may just be a big survey, such as Pomeroy's Ancient Greece.