...When examining the idea of the cause of a particular (finite) thing I believe we must consider two aspects of that thing, its essence and its existence.

   As you have pointed out, the cause of the existence of a particular (finite) thing is shown by Spinoza in E1P28 to be some other finite thing, etc. and this being so, God has the idea of the whole chain of causes (the "common order of nature"). Keep in mind that God does not have this chain of ideas in the way that we might endeavor to imagine it, that is in "time". The ideas of individual things in "the idea of God" (see E2P3) are all clear and distinct and eternal whereas in our mind we cannot have these ideas as adequate. For us, even the ideas of our own particular body/mind, as to it's existence are not adequate. Spinoza indicates:

===== E2P29Cor =====
"Hence it follows that the human mind, when it perceives things after the common order of nature, has not an adequate but only a confused and fragmentary knowledge of itself, of its own body, and of external bodies."
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   This difference between our mind and "the idea of God" seems to be illustrated quite nicely by Spinoza in:

===== E2P11Cor.=====
"Hence it follows, that the human mind is part of the infinite intellect of God.
Thus when we say, that the human mind perceives this or that, we make the assertion, that God has this or that idea, not in so far as he is infinite, but in so far as he is displayed through the nature of the human mind, or in so far as he constitutes the essence of the human mind; and when we say that God has this or that idea, not only in so far as he constitutes the essence of the human mind, but also in so far as he, simultaneously with the human mind, has the further idea of another thing, we assert that the human mind perceives a thing in part or inadequately."
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   Ok, so far we might be able to reason (as Spinoza did) that God has the ideas of all things including therefore the causal chain but we cannot ourselves follow that actual chain of causes. When I first read this and thought about it in my own confused way I was disappointed because I wanted to follow that chain! It's kind of like the inhabitants of Plato's Cave wanting the fellow who claims to have been "outside" (whatever that is) to show them what he's talking about by displaying shadows on the wall. Continued study of Spinoza's ideas however has revealed something better with which the mind can occupy itself than chasing shadows. So what good is this idea? Let's go on to your second question and it might become more clear.

   You ask: "What are the differences between the existence of a particular thing and the duration of that thing?" I think if we start with Spinoza's definition of duration we might see more about his view on this.

===== E2: DEF. 5: =====
"Duration is the indefinite continuance of existing.
Explanation.--I say indefinite, because it cannot be determined through the existence itself of the existing thing, or by its efficient cause, which necessarily gives the existence of the thing, but does not take it away."
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   For me this often becomes confusing because my imagination wants to "picture" this. He's defining duration with "continuance" and I blend that back into "time" in my imagination. However, thinking about our first discussion above on the chain of causes (or "the order of nature") we can perhaps reason that given any particular collection of particular things (let's say the Earth) the order of nature whereby each particular thing in that collection is found to be in a particular relation to the other things (for instance, from our view we say our body reaches a certain age) is not "strung out in time" in the "idea of God". The "idea of God" is eternal and does not involve time. Time is a confused idea we form through the operations of our imagination and it does not adequately represent to us the "idea of God". Spinoza, expresses this in:

===== E5P29, Note. =====
"Things are conceived by us as actual in two ways; either as existing in relation to a given time and place, or as contained in God and following from the necessity of the divine nature. Whatsoever we conceive in this second way as true or real, we conceive under the form of eternity, and their ideas involve the eternal and infinite essence of God, as we showed in E2P45 and E2P45N, which see."
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   The note he referred to above may help answer your question and more importantly help to point out the direction in which Spinoza is leading us:

===== E2P45 =====
"Every idea of every body, or of every particular thing actually existing, necessarily involves the eternal and infinite essence of God.
Proof.--The idea of a particular thing actually existing necessarily involves both the existence and the essence of the said thing (E2P8). Now particular things cannot be conceived without God (E1P15); but, inasmuch as (E2P6) they have God for their cause, in so far as he is regarded under the attribute of which the things in question are modes, their ideas must necessarily involve (E1A4) the conception of the attribute of those ideas--that is (E1D6), the eternal and infinite essence of God. Q.E.D."
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===== E2P45N =====
"By existence I do not here mean duration--that is, existence in so far as it is conceived abstractedly, and as a certain form of quantity. I am speaking of the very nature of existence, which is assigned to particular things, because they follow in infinite numbers and in infinite ways from the eternal necessity of God's nature (E1P16). I am speaking, I repeat, of the very existence of particular things, in so far as they are in God. For although each particular thing be conditioned by another particular thing to exist in a given way, yet the force whereby each particular thing perseveres in existing follows from the eternal necessity of God's nature (cf. E1P24C)."
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   Many people seem to pass over too quickly Spinoza's caution to avoid abstractions and, of equal importance, to avoid confusing "things of reason" with "real beings". It was not until I set aside my desire to form an abstract image of God and of a general type of "man" and began to examine my own particular nature that the following proposition came to life for me:

===== E5P30: =====
"Our mind, in so far as it knows itself and the body under the form of eternity, has to that extent necessarily a knowledge of God, and knows that it is in God, and is conceived through God.
Proof.-- Eternity is the very essence of God, in so far as this involves necessary existence (E1D8). Therefore to conceive things under the form of eternity, is to conceive things in so far as they are conceived through the essence of God as real entities, or in so far as they involve existence through the essence of God; wherefore our mind, in so far as it conceives itself and the body under the form of eternity, has to that extent necessarily a knowledge of God, and knows, etc. Q.E.D."
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   He is saying no less than that we can know, to a certain extent, the essence of God in so far as we come to know our own particular essence as a real entity, not through some abstraction and not even through reason but intuitively, that is, directly. When we come to know ourselves in this way, to whatever extent, we are joined to that which is eternal (existence itself, timeless, not infinite in duration) and infinite!

   Note that the entire Ethics is a work of Reason (the second kind of knowledge) and as such we can know the ideas to be true. However, Spinoza's aim is to bring the mind into direct union with its essence (God) through Intuition (the third kind of knowledge). In this regard he points to the vast difference between the two ways of knowing in:

===== E5P36Note =====
... Again, since the essence of our mind consists solely in knowledge, whereof the beginning and the foundation is God (E1P15 and E2P47N), it becomes clear to us, in what manner and way our mind, as to its essence and existence, follows from the divine nature and constantly depends on God.
   I have thought it worth while here to call attention to this, in order to show by this example how the knowledge of particular things, which I have called intuitive or of the third kind (E2P40N2), is potent, and more powerful than the universal knowledge, which I have styled knowledge of the second kind. For, although in Part 1 I showed in general terms, that all things (and consequently, also, the human mind) depend as to their essence and existence on God, yet that demonstration, though legitimate and placed beyond the chances of doubt, does not affect our mind so much, as when the same conclusion is derived from the actual essence of some particular thing, which we say depends on God.
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...I will confess that I came to Spinoza not through an academic path but through an inner quest for something --though I knew not what it might be at the time. It has only been after long self-study, using Spinoza and a few other's writings for guidance, that the "Eternal Light" has "begun" (from the viewpoint of my imagined life) to dawn.

    Yours in Inner Friendship,
      Terry