Itô formula's proof

Question

it's about the proof of the Itô formula

Here I give the proof (I marked the lines with my issues in colours)

1. How do we use a/the usual stopping argument?

2. How do we use Lemma 4.51?

2a) We use the variance process $[X]_s$ . Why is it possible to extend it to a covariance process $[X^i,X^j]$. (I can see that we have to consider more dimensions but why is it possible to do it that way?)

2b) And how does the Itô-formula exactly follow for result follow from the implication $(H^n ° X) \rightarrow (H°X)$ of Lemma 4.51?

2c) Are polynomials always predictable?

3. Why is $Y$ a semimartingale?