Yes. "The car that just passed was theirs" is grammatically correct.
"July has just been started" is not correct grammar, instead the correct grammar is "July has just started."
Both are correct. Most people use the latter.
The sentence "I got here just 2 minutes before their cut off time" is correct grammar.
For more than 20 years of existence i just now had the time to visit here is not a correct grammar.
It would be better to add "have." The concert to which you have just listened was the same one you once heard as a child.
I have / I've just seen you do it. (so none of your variants).
Yes, your grammar is correct. Your sentence "Just take care on your way home" is a polite way to tell someone to be safe while going home.
The correct grammar is YOU AND I if used as a subject, e.g. ""You & I will have a jolly good time". Correct grammar requires YOU AND ME if used as an object, e.g. "This is just between you and me" "I" designates a subject and "me" designates an object.
Patients' diabetes. (just spell or grammar check it)
The colloquial phrase is "most probably" and in correct grammar is just "probably."
"For so many years of existence i just now had the time to visit here" is not correct grammar "For many years of existence,I now have the time to visit here."
No, the correct phrasing is "It was said that she and Nick were just good friends." The subject pronoun "her" should be changed to the subjective pronoun "she" to maintain correct grammar.