I have realized that it would be quite difficult to analyze the Gods relations to each other unless I first analyze how I relate to the Gods and view them, and have come to know them at this time in my life. I'm sure that as I grow older and gain more experience with them and more knowledge of them my views will change, but here I go anyway.
First I am tackling what should be tackled first, the King. Zeus is a multifaceted and complex God as is reflected by his various epithets, a few of which include "Of the Rain" "Savior" "Giver of Good" "Warlike" "Of the House" and "Contriver" to give you just a very shallow and quick idea of the diversity of his roles. They extend beyond these though, and his epithets are many and varied.
Who is Zeus then? He is the King of the Gods. Through Zeus things come to fruition I believe. This is not to say that he is all powerful, but the other Gods do not do things if they go against his will and desires (whatever those may be). He is regarded as a very wise and just God, so his decisions are to be trusted. Now, this does not mean that I think Athena and Aphrodite and Dionysos are all checking in with Zeus 24/7 for every single one of their actions, but I do think that the Gods are wise enough to know what would and what would not violate the will of Zeus and thus because of his position as king they respect and obey his decisions. So I, in turn, definitely see him as king of the theoi and I trust that he makes fair, just, and wise decisions most of the time.
I also find him to be a very difficult God to understand. In worship and when I simply pay respect I often feel nothing during the rite (except for gratitude of course). I feel no stirring or presence within me usually, and whenever I do whatever stirs up is just a confusing feeling. Sort of like I can't understand something or comprehend it, but not quite that. From that, I've come to see Zeus as a very mysterious and powerful God, yet also a distant one. I'm sure there are folks who feel quite close to Zeus and frequently feel his presence at their rites, but I am not one of those folks. For me he is almost as distant as Yahweh was, except Zeus has actually graced my rites with his presence on a couple of occasions.
In terms of function I largely view Zeus as the protector of my house, I believe he has the ability to influence (but not control) the weather. I believe he (like most of the Gods) can give us courage and strength, and can help us pull through times of intense hardship or other extremely difficult situations (one of his epithets is Savior, remember?). He, with Hera, also governs marriage in its more pragmatic aspects, the functional aspects of it that while perhaps not as exciting or as passionate as love, are none the less vital to a marriage being successful (at least from what I've seen of relatively happy and lengthy marriages). I also view him as having some influence and sway on male virility and potency. And to these things a number of other things, such as protection, wealth, prosperity, luck, happiness, and justice.
All that aside though, Zeus is Zeus, and even him I make certain lines and see him as certain things, I'm certain he is much more than that. I, after all, am but a man and he is a God. I'm almost certain he exceeds the things I've assigned to him, and I'm quite satisfied with knowing that my understanding of him will continue to change and grow. I do, after all, love to learn.