So Mote it Be is a type of Command to signify the ending. It's like Amen at the end of a prayer.
Thee, thou, thine, Thy, are all old English words that are used to aid in giving the spell you are doing more of a deeper feeling, to help in a rhyming process etc... these words are used for different reasons, in different cases, and by very different people
This may help a little so you know what each means
More accurately, that's the second person singular pronoun.
'Thou' corresponds to 'I/you/he/she'. (Nominative)
'Thee' corresponds to 'me/you/him/her'. (Accusative)
'Thy' corresponds to 'my/your/his/her'. (Possessive)
'Thine' -- 'mine/yours/his/hers'.
It's an archaic form, and its status was similar to the French vous/tu. At one time, it was the formal form, but became the familiar form around Shakespeare's time.
As for the archaic plural form...
Nominative / Accusative / Possessive
Ye (or you) / you / your, yours