1. Remember, the most important thing about you doesn't change.
2. Remember that the most important thing about you doesn't change.
(Does #1 mean #2?)
3. She is taller than me.
4. She is taller than I.
5. She is taller than I am.
6. She is taller than I am tall.
(Can we use all the four expressions? What is the difference among them? Which ones are frequently used?)
Yes, #1 and 2 mean the same thing.
#3 is incorrect. you would not say "me am" so you can not say than me.
#6 is never used.
Both $4 and 5 are used.