4) how do we know that Mr Birling feels inferior to Gerald's family?

The women leave the room, and Eric follows them. Birling and Gerald discuss the fact that Gerald might have “done better for [himself] socially”: Sheila is Gerald’s social inferior. Birling confides to Gerald that he is in the running for a knighthood in the next Honors List. When Eric returns, Birling continues giving advice, and he is passionately announcing his “every man for himself” worldview when the doorbell rings.

Mr Birling understands why Lady Croft might prefer Gerald to marry from within his own class. He uses the possibility of a knighthood to impress Gerald and, throughhim, Lady Croft