Angel of the LORD

In the Old Testament, somebody called 'Angel of the LORD' shows up a lot. Sometimes, this person/angel confuses the understand the characters in the story. In Genesis 22, it was 'the Angel of the LORD' who stopped Abraham from killing Isaac. Also in Exodus 3, 'the Angel of the LORD' calls Moses from the burning bush.

In either passage, the following portion suggests that the one who is present is the LORD Himself. 

As I was checking the translation of both stories, there seems to be some confusion of character. A word/sign used for 'Angel of the LORD' is something like a being which has a wing, so this being is considered a different being from the LORD Himself. But, this being talks as if he is the LORD.

The word 'Angel' has a very strong imagery, the being with wing, and in many cases that's a female like figure. It might be this 'image' the translators had when they were translating these portions.

The word 'angel' is from 'αγγελος' in Greek and in either Hebrew or Greek, they mean 'messenger.' In the OT passages above, 'Angel of the LORD' is 'מלאך יהוה’, and again, this should mean 'the messenger of the LORD.' In NT, equivalent expression would be 'αγγελος κυριου'. So, now what can be 'messenger'? Does it have to be a being? 

I have never come across in NT that 'αγγελος' denote non-being (I might be wrong, but that's my observation). 

According to the Word Biblical Commentary, in many part of Pentateuch, this expression of 'the angel of the LORD' can mean the sign/symbol/representation of the LORD. That means, this 'angel' may not mean a being apart from the LORD, rather it is part of the LORD. So, it may be like the Sun and the radiation from the Sun. The Sun is understood to be the LORD and the radiation as the messenger... 

That would solve the problem of understanding, but it would be still difficult to translate... I guess. 

Hearing way or Deaf way?

The word 'translation' is perceived so vague to some that it requires a modifier to restrict its meaning often times. Sometimes we say 'literal' translation, and other times, 'meaning-based' translation, or 'dynamic-equivalence'... and so on.
In many cases, I'm not sure how 'literal' one can translate. Each word has multiple senses and it is not likely to find word-to-word match up in cross-language translation. Also When the bible is translated into other languages, word order matters, too. Hebrew basic word order is VSO and Greek basic word order also is VSO (though Greek is highly flexible in word order). If, for example, we translate the bible into Japanese which is a SOV-basic-word-order-language, it is already not 'literal' once we change its word order. But if we retain the word order of the original language, it will cost the comprehensibility of the translated text.
Also as I have studied Discourse of languages, it matters how we use structures like repetition, chiasm, fronting the words, information load, pronoun use... so on. Depending on how we use them, it changes the force, focus, emphasis, hesitation... many things so the reader/audience gets different concepts.
If 'literal' risks the accuracy of what the text means, then the meaning should (in my opinion) be retained and changes the literal-ness of the text.

So, now here is an example I have found today. It is from Exodus 3:4.

3:4 When the LORD saw that he had turned aside to see, God called to him out of the bush, “Moses, Moses!” And he said, “Here I am.”

When the LORD calls Moses, He calls Moses' name twice. It is so natural for the Hearing folks. But for the Deaf, it is not the case. At least, here in the Philippines, the Deaf taps, never calls people's name.
Their first draft had this "Moses! Moses!" in their translation. But they'd probably change it to "Tap Tap." In hearing way, it sounds like "Hey hey!" This is a little funny example, but that's how things are different in different language, I think.
I have heard a message once from this passage that the LORD knows the name of Moses!! It may be a good message, but I don't think that's really meant here.