My answer will depend on a completely different understanding and translation used here:
Now the serpent was more subtil than any beast of the field which the LORD God had made. And he said unto the woman, Yea, hath God said, Ye shall not eat of every tree of the garden?
Notice this word Yea is translating two Hebrew words: אף כי (aph ki). It is very worthwhile to look up its use and translation all through the OT. It seems to be a way of saying... "on top of that", or "furthermore" or "much more/less than"...
For I know thy rebellion, and thy stiff neck: behold, while I am yet alive with you this day, ye have been rebellious against the LORD; and how much more after my death?(Deu 31:27)
When one told me, saying, Behold, Saul is dead, thinking to have brought good tidings, I took hold of him, and slew him in Ziklag, who thought that I would have given him a reward for his tidings: How much more, when wicked men have slain a righteous person in his own house upon his bed? shall I not therefore now require his blood of your hand, and take you away from the earth? (2Sa 4:10-11)
But will God indeed dwell on the earth? behold, the heaven and heaven of heavens cannot contain thee; how much less this house that I have builded? (1Ki 8:27)
Fine speech is not becoming to a fool; still less is false speech to a prince. (Pro 17:7)
And furthermore, that ye have sent for men to come from far, unto whom a messenger was sent; and, lo, they came: for whom thou didst wash thyself, paintedst thy eyes, and deckedst thyself with ornaments, (Eze 23:40)
אף כי (translated here as "Yea"), is simply not used to start a conversation or a thought but used to compare something with something that has just been said in greater intensity.
This suggests that we are catching them in mid-conversation, at its back-end apparently. What were they talking about before?
Looking at the remainder of their conversation:
And the woman said unto the serpent, We may eat of the fruit of the trees of the garden: But of the fruit of the tree which is in the midst of the garden, God hath said, Ye shall not eat of it, neither shall ye touch it, lest ye die. And the serpent said unto the woman, Ye shall not surely die: For God doth know that in the day ye eat thereof, then your eyes shall be opened, and ye shall be as gods, knowing good and evil.(Gen 3:1-5)
"gods" is a perfectly good translation here, and choosing "God" instead depends on interpretation not translation. I will go with "gods" as the Greek Old Testament does and every English Translation up until the Revised Version.
Now, it always struck me as odd that she was intrigued at the idea of being as the gods knowing good and evil. How does she know anything about them or what it is like to know good and evil? She does not ask any questions about it, she seems to know exactly what he is talking about...
My conjecture is that he has been telling her about them, and about himself as one of them: "one of the gods that knows good and evil", and how that he is part of a divine class of beings called gods and sons of God by the Most High, and set as judges over the earth... and tempting her that she can be like him/them by eating of this fruit.
Are there such beings: gods that know good and evil?
It does appear from Psalm 82 that there is a heavenly court called the congregation of the mighty with celestial judges who the Most High God appointed as judges and calls gods, and even children of the Most High.
Psalm 82: A Psalm of Asaph. God standeth in the congregation of the mighty; he judgeth among the gods. How long will ye judge unjustly, and accept the persons of the wicked? Selah. Defend the poor and fatherless: do justice to the afflicted and needy. Deliver the poor and needy: rid them out of the hand of the wicked. They know not, neither will they understand; they walk on in darkness: all the foundations of the earth are out of course. I have said, Ye are gods; and all of you are children of the most High. But ye shall die like men, and fall like one of the princes. Arise, O God, judge the earth: for thou shalt inherit all nations. (Psa 82:1-8)
Could this be what the sons of God refers to of whom Satan was one?
And the LORD God said, Behold, the man is become as one of us, to know good and evil: and now, lest he put forth his hand, and take also of the tree of life, and eat, and live for ever: (Gen 3:22)
That the sons of God saw the daughters of men that they were fair; and they took them wives of all which they chose.(Gen 6:2)
Thou shalt not revile the gods, nor curse the ruler of thy people. (Exo 22:28)
Now there was a day when the sons of God came to present themselves before the LORD, and Satan came also among them. (Job 1:6)
In whom the god of this world hath blinded the minds of them which believe not, lest the light of the glorious gospel of Christ, who is the image of God, should shine unto them. (2Co 4:4)
If so, it would make sense of what the content was of the conversation between the Serpent and Eve prior to what has been recorded here. And also what she was tempted with: not to be as God knowing good and evil, in whose image she is already created (in likeness not knowledge), but to become as one of the gods who had knowledge of good and evil in order to stand as judges over the earth.
And to answer OP's explicit questions:
Eva must have known she is in the image of God, but that does not mean she was "like" God. She was in "in our image, after our likeness". That does not mean man (and woman) was in every respect "as him", since God himself said, "now man has become as one of us" in this aspect, after the fall.
It is reasonable and proper to assume that Eve surely would not have had a concept, reference or experience of evil prior to her conversation with Satan. So other than what the Serpent may have tried to convey to her in whatever they had been talking about prior to our us entering in on their discussion, we can and should assume se had no knowledge of evil. Maybe, similar to animals, morality (knowledge of Good and Evil) was simply not a concept in her mind.