[RPG] Do you get a proficiency bonus to AC

Proficiency bonus is noted in your character advancement table (in Character Creation file, or PHB p.15) as "Proficiency Bonus", and that is universal for your character level. For example, according to the table, a 3rd-level character gets +2 for proficiency bonus, because the table says so. For convenience of single-classed characters, you can also look up your proficiency bonus for your level in your class advancement table.

Thus, a 5th-level Fighter with Strength 18 (modifier is +4) wielding his greatsword makes attack roll with 1d20+4 (Strength modifier) + 3 (proficiency bonus at character level 5) = 1d20+7.

If you are proficient with a weapon, you add your proficiency bonus to attack rolls with that weapon. The spell does not change that. Warlocks are proficient with simple weapons, which includes the quarterstaff, so yes.