NOT A TEACHER
Hello, Katherine:
Let's discuss "just" later.
1. She has red hair like/as I do.
a. In that sentence, "as" is the preferred conjunction.
b. "Like," however, is widely used by native speakers as a conjunction.
c. It is your call as to which word you wish to use. (I shall keep my choice to myself.)
d. As you know, after a conjunction, you need a sentence, such as "I do."
e. As you also know, "I do" is a shorter way to say "I have red hair."
2. "She has red hair like me."
a. In this sentence, we are dealing with "like" as a preposition.
b. As you know, a noun or pronoun comes after a preposition.
THUS, you have three fine choices:
"She has red hair as I do."
"She has red hair like I do."
"She has red hair like me."
("She has red hair like/as I have red hair" would NOT sound natural.)
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3. "He came just as I was leaving."
a. House and Harman in their Descriptive English Grammar (1931 and 1950) say that "just" modifies "as."
4. ""You always want something just when I am leaving."
a. Pence and Emery in A Grammar of Present-Day English (1947 and 1963) say that "just" modifies the whole clause of "when I am leaving."
What does "just" modify in your sentence? I will keep my opinion to myself.
Have a nice day!