Alright first things first: Humanity is made unto the image of God:  Not in form.  This is evident once you realize that both males and females are human, and not the same in physical form, and since there is variety in both sexes -  Only 1 God, not billions.
 

If by properties, you mean knowledge, that doesn't make very much sense...  The soul of a human is what is made in the image of God.  That doesn't mean our souls are Gods, its just like a statue of a person is made in the image of a person.

As animals are not sentient beings, they can't sin.

Animals are not subject to morality, lacking a soul:

Where in the Bible does it say humans would not sin without the knowledge of sin?  Perhaps it does, but I'm not aware of the verse or chapter.

Adam and Eve eat the Forbidden Fruit and, thus, are cast out of Eden:

The arguments here are built on the conjecture of the first, so until those are confirmed these can barely be considered hypothesises.

Initially, I think it's best to clarify what relevance my answering these questions has to the status of my theism - I don't identify as a the kind of person one would generally call a christian creationist. I follow no dogma in either category and I do not have any affiliation with nominal religion regarding creed or character. I'm a free thinker and my brand of theism is probably best described as philosophical panentheism. So, in relation to my beliefs, creation mythology and other theological revelation has intrinsic truth value whereby I believe that there is substance to the claims of an order which may be described as 'divinely spiritual' having involvement in the establishment of sacred tracts.

And to the question, I would answer that the image implied by Genesis of God which man is not distinct in terms of form or property, it is therefore, both. 

In that case it follows directly that I agree with you on 2, humans do know what sin is, I would submit that we are able to know that knowledge of sin or error is intrinsic to humanity via the permutations of the human experience known as emotion. Emotion is spontaneous and reactive, emotion, you could say, is in direct communication with subjective and objective human experience and therefore it forms part of human awareness of it's condition. There are emotions in the gestalt of human experience which deal directly with the condition of percieved error or evil - namely guilt, shame, compassion - in this way we can link the emotional awareness of humans to the direct awareness of the nature of sin.

To point 3 - the image in form is physical as you have proposed, however I submit that we would err to limit this description with a concept of human physicality which is incomplete. The standard anthropomorphic concept is just such a limited description. Humans as discrete biological beings which begin and end at classical material extremities is false regardless of your epistemology. If you are a materal monist then your actual being is defined as an emergent pattern from the sum of all universal interactions converging at your position in time and space. Therefore you are the universe, you are not distinct from it because you are not determined in a vacuum distinct from it. Likewise if you are a dualist or neutral monist your being is determined from the seat of your unconscious mind, not just your conscious one, therefore to define oneself confined within the limits of human conscious sentience is incorrect. 

In this way, either way, as a neutral monist I have the luxury of claiming both, we are completely and undeniably created in the image of a pan or panen- deity.

I don't believe that animals do not have a soul, at the least they are part of any human's being and soul, we do not exist without them.  Supposing you wish me to describe a difference between humans and animals in terms of my theology it is this - the conscious animal mind and physical being is structured differently to the human mind because animals emerge from the common thread of this existence, from God, at a different level to humans. The animal condition emerges at a convergence of conditions distinct from one at which a human emerges. Where the human I emerges the surrounding conditions in combination with the arising conditions (for brevity I will use 'coordinates' in future to refer to this combination) mimic those of our "god" being to which we aspire theologically, therefore human coordinates are "godlike" coordinates the condition of these coordinates is phenomenally sentient and phenomenally potent. Animal coordinates correspond to a physical position of sentience and potential overwhelmed by that of humans. This does not mean they don't have a soul, it means they are a different part of one, not the driver seat part - therefore not God's image. Animals then are subject to a morality appropriate to their order of power and sentience which naturally due to the extremes of power and knowledge available to us does not closely resemble the degree to which humans are be responsible for their actions.

You do not need to know what sin is in order to do it, either knowledge or ability can arise independently of each other.  So yes, Adam and Eve could sin without knowing that they had done that is logically plausible IMHO.

Preempting your follow up question to this, one of my main objections to chritsian institutionalised religion is the melodrama over the concept of sin. The anthropomorphised limited concept of the human condition dictates unreasonably on the subject of the human condition in "original sin". Genesis does not say humans fell from grace, the bible does not say humans fell from grace, christian dogma says this without basis. The book this 'fall from grace' is suposedly taken from is ironically filled with reassurances that humans are still in the grace of god as to having knowledge of good and evil, it is not a theological truth that knowledge has taken grace from humanity. It is rather, the point that humans with knowledge are capable of taking this "grace" from themselves. 

To cut a long story short, basically people make too big a deal of original sin (and original redemption for that matter) these are simply representations of embedded selections in the interactions surrounding one's coordinate position. They describe our condition accurately as they are, without extraneous dogma and interpretation. It is not intrinsically disgraceful that we our existence is positioned within the possible world emerging from the original pursuit of knowledge, nor is it intrinsically special either that we are positioned likewise in relation to a divine exemplar, it just is. This is the condition and Genesis/NT is philosophically explanatory, not autocratic or dictatorial.

2. Yes, this is the likely reality, however I do not subscribe to the melodramatic dogma of sin peculiar to christian institutions so I can say that and also say that my existence emerges into knowledge in the due course of things, the 'sin' of genesis comprises who I am, thereforewho I am would not be to be destroyed by sin if it weren't for the sin of knowledge existing.  The sin is therefore a grace on my human existence in this coordinate, for such 'time' as this coordinate is relevant to my identity.

3 - is of no consequence to my theism at all, I am not in mortal conflict with my deity.

 A short definition (and subject to qualification) might be that humans possess all of the attributes of God that may be communicated to his creatures

The bible says very little about animals.  Not sure who says animals lack a soul .

Sin is sin. You don't need to what sin is to sin.

1. Couldn't and won't are two different things.

2.  Huh? what?  Yes if you hate justice worshiping God probably not up your alley.