Verse 19 already said that Mordechai sits b'Sha'ar ha'Melech. Why is this repeated?
Malbim: The verse shows how Hashem prepared the cure before the illness - like a blood-letter prepares to revive the patient before letting blood. "Ani Hashem Rof'echa" (Shemos 15:26) - I do not put illness on you like on Egypt, which was to punish the Rasha, rather, in order to cure you. The first preparation was making Esther queen. The second was merit for Mordechai, that he saved the king's life. Mordechai sat in grandeur and honor. This aroused envy of those who stand and guard, and enabled him to hear the plot.
Why did Bigsan and Seresh get angry?
Torah Temimah citing Megilah 13b: Hashem angered servants on their master to do a miracle for a Tzadik, i.e. Mordechai - "... and the matter became known to Mordechai."
Refer to 2:16:2:2*.
Torah Temimah citing Esther Rabah: Achashverosh demoted them, and seated Mordechai in place of them.
Malbim: Hashem arranged it; it was for no reason.
Why does it say "mi'Shomerei ha'Saf"?
Vilna Gaon: There are three Shomerei ha'Saf, like it says (in Melachim II, 25:18).
Malbim: Usually they choose for this those who love the king. Hashem arranged that they get angry at him for no reason. Since they were Sarisim, why should they envy Mordechai's grandeur? Sometimes Sarim rebel against the king, in order that one of them will become king - Sarisim would not do so. They know that they will be killed for this!
How did they intend to stretch their hand against the king?
Rashi: They would give to him poison to drink.