Do Polearm Master and Warcaster Work Together?

Yes, the combination "quarterstaff + War Caster + Polearm Master" allows you to cast Booming Blade when someone enters your reach.

Does booming blade work with Warcaster?

The Booming Blade spell continues to work with the War Caster feat. The spell targets one creature.

Does polearm master work with Glaive?

Polearm Master lets you make an attack with the opposite end of a glaive, halberd or quarterstaff; the former two have the heavy property. Thus, they can use both feats with a glaive or halberd.