Are the sentences "What if she had spoken so that everyone had heard?" and "A year ago, the teacher would have respected her because she new English well" correct?

Question

Answer

Using the past perfect ("had heard") after "so that" is unnatural here. "So that" introduces a purpose or result. When the main clause is in the past perfect ("had spoken"), the "so that" clause typically needs a past modal (like could or would) to show the intended or potential result.

The Correction depends on your intended meaning:

If you mean her goal was to make them able to hear:

"What if she had spoken so that everyone could hear?"

(This implies she didn't speak loudly/clearly enough in the past.)

If you mean her goal was to make them actually hear (a factual result):

"What if she had spoken so that everyone heard?" (simple past)

OR, more naturally, for a hypothetical past:

"What if she had spoken so that everyone would have heard?"

For a past hypothetical scenario, the clearest option is:

"What if she had spoken so that everyone could have heard?"

In the second sentence, ignoring the error of using "new" instead of "knew", the sentence is fine and understandable.

Answer

It's "knew English" not "new English".  "Knew" and "new" are 'homophones'.  They are both English words and are pronounced the same.  A good lesson in the trickier parts of English! There is a pattern here:
Present tense         Past tense
"know"                     "knew"
"blow"                      "blew"
"throw"                     "threw"
but these  " ---ow" words don't follow it: "mow"  "follow" "sow" [which has two different meanings, one of which is pronounced like "how" or "bow" (which also has two different meanings!!) ].   Wow!  Why can't we all just learn Loglan?