1. How are objects ontologically prior to relationships? Is it that because objects are unreachable in a phenomenological way, we acknowledge the existence of such objects in themselves that we can't acknowledge in any further way? - That is to say, we know there's an actual object, but since we can't access it, we can say nothing more about it than that?
Objects are reachable phenomenologically. But never exhaustively. Hitting a stone with a laser may turn it to powder--but that doesn't access the stone as stone. In fact now you have a million problems where before you had just one: instead of a single stone, you have millions of particles of powder!
We can say loads more about objects than just the fact that the exist. Objects aren't just hunks of whateverness: they are lizards, Rubik's cubes and the Oort Cloud.
The best way to think about "withdrawal" is that things are so specific, so unique, that they can't be totally specified or accessed by anything. Even themselves.
The other thing is that frogs, butter knives and protons also get to say things about objects, not just humans...
i. Causality as "in front" of objects- What does "in front" mean?
It means ontologically in front, not spatially. Objects are prior to relations, which is where causality lives.
2. You say that there is no environment - no middle space in which everything floats. What, then, becomes of Harman's intermediary in his argument for "vicarious causation" and his plate tectonics of ontology? Or is this a mystery, too?
Harman's intermediary is also an entity that is not more real than other entities. Concepts such as world and environment are reductive in that they are taken to be more real than what comprises them.
Another way of looking at it is that, if everything has a world (crystals, trees, bunny rabbits) then nothing does. World is the sort of concept that belongs to one or a few things, because it is normative. Heidegger says stones and lizards lack a world or are "poor in world." Humans have worlds because they are better at making things real, for Heidegger.
3. I was talking about OOO to my philosopher friend, who does not believe in essence, and I realized I don't really know how to explain the rift between an object's appearance and its essence.
It's a very tricky concept. I am embarking on a longer term book project called Weird Essentialism just to explain it to myself! But you can tell your friend something like this: almost every Western philosophy makes a distinction between essence and appearance that involves a metaphysics of presence. This means that the essence of a thing is more real than its appearance, and that this realness means being constantly present. Underlying the appearance of this blue mug is an actual thing that doesn't change (as much): atoms, some kind of form, eidos, and so on.
For Plato and all the rest there should be a clear dotted line between essence and appearance: your job is to be able to separate essence from appearance. I'm arguing that they are inseparable although they are different.
4. What is an object? Is everything an object? Are ideas objects?
An object is a thing that has a rift between its essence and its appearance, a rift that makes it appear contradictory in some way. If a thing doesn't have that it isn't an object. Ideas are objects. I sometimes say "entity" or "being" just to lose the prejudice we all have about the word "object."
5. Is everything becoming - not being?
Becoming is just another metaphysically present thing--something taken as more real than the things that temporarily poke out of it. This is basically why Heidegger thinks Nietzsche had it wrong. Nietzsche substituted a metaphysics of presence based on somewhat static things for one based on somewhat fluid things. But fluidity doesn't make you more real than stasis. There is a popular prejudice nowadays that it does.
6. Do essences ever die? (Is this why one can never kill oneself?)
Essences die all the time, which is why things happen. You can't kill yourself because the you who is killing yourself is different from the you who is killed. But in another sense, suicide does happen all the time just because things really are fragile. Essences collapse into appearances, that is what dying is, in this philosophy. Even a black hole, from which nothing escapes, eventually evaporates because of its appearance (Hawking radiation). In the end, the appearance of a thing is fatal to a thing.
7. If the future is withdrawal, and poems are of the future, how do they happen? Does this have anything to do with the birthing of new objects, which happens outside of time?
Poems are train stations where the past slides against the future, not touching. The essence or meaning of a poem is (in) the future. The form is (in) the past. Poems happen, sometimes, when a human creates a really nice train station for the trains to slide past one another. A poet allows the past to slide against the future... There are lots of ways to make this happen. One way is to cause words and phrases to malfunction.
This does help to think about novelty (which is your second question). A new thing is a whole new temporality, and so it's "outside" time to the extent that it's not anything else--and time just is a thing that flows out of objects. There are no objects "in" time at all.