How many basic operations are there in an algorithm for the simple multiplication of two numbers of equal length?
It's hard to tell what anyone means by "comparable" in a specific context. I would take it to mean "of the same order", so something like $n^2$, maybe $100\cdot n^2$ or $0.0001\cdot n^2$, but not $n$ or $n^3$.

The final addition is doing (roughly) $n$ additions of numbers of (roughly) non-$\_$ $n$ digits, and each of those additions takes (roughly) $n$ additions of single digit numbers. So that's why you end up with (roughly) $n^2$ additions.