Question

I am looking for a concise explanation of HEN and HEIS, particularly what causes each form to be written and what affects the meaning of the word. I need to understand how to tell when HEN means one as in number and when it means symbolically one or one in essence or purpose.

This is related to trying to understand why HEN means one is essence in John 10:30 but means one in number in Mat 5:18

I know it must be related to the noun genders but want to understand this more fully from an expert such as yourself.

Answer 1

Both of them mean one.

εἷς, μία, ἕν are the three genders (male, female, neutral respectively) of the ancient Greek word.  In modern Greek we say ένας, μία ένα.  

Mat 5:18:
ἰῶτα ἓν ἢ μία κεραία οὐ μὴ παρέλθῃ ἀπὸ τοῦ νόμου
Here it means one.

John 10:30:
ἐγὼ καὶ ὁ πατὴρ ἕν ἐσμεν.
Here it says "me and my father are one".  It means indivisible.

This is the exact same meaning as in Mat 19:5:
...καὶ ἔσονται οἱ δύο εἰς σάρκα μίαν;
It means that after marriage the man and the woman become one, a single body, so strong that nobody can separate them.

There are no grammatical rules for this.  It is just an expression.

References:  
https://el.wiktionary.org/wiki/%CE%B5%E1%BC%B7%CF%82
https://www.biblegateway.com/passage/?search=Mat+5%3A18&version=SBLGNT
https://www.biblegateway.com/passage/?search=John+10:30&version=SBLGNT
https://www.biblegateway.com/passage/?search=%20%CE%9A%CE%91%CE%A4%CE%91%20%CE%9C%CE%91%CE%A4%CE%98%CE%91%CE%99%CE%9F%CE%9D+19:5&version=SBLGNT

Comments

I think Between "heis" and "monos(John17:3)" should be compared not "heis" and "Mia" or "En"