HexBlade Warlocks give you proficiency with shields:

Hex Warrior

At 1st level, you acquire the training necessary to effectively arm yourself for battle. You gain proficiency with medium armor, shields, and martial weapons.

Can a Warlock (with Warcaster feat) use both staff (only for casting, never melee attacking) and a shield to increase AC? and how to deal with staffs that gives you extra AC like Staff of Power?

Staff of Power

DMG Staff, Major, Very Rare (Requires Attunement by a Sorcerer, Warlock, or Wizard) 4 lbs.

This staff can be wielded as a magic quarterstaff that grants a +2 bonus to attack and damage rolls made with it. While holding it, you gain a +2 bonus to Armor Class, saving throws, and spell attack rolls.

Can a warlock with

Shield +1 [+3 AC]

Staff of Power [+2 AC]

Half Plate Armor [AC 15 + Dex (max 2)]

Reach 15 + 2 + 2 + 3 == 22 flat AC? and have all the benefits given by the staff? (and he can still cast Shield spell to reach 27 AC)

Hexblade warlocks gain proficiency with shields at 1st level from the Hex Warrior feature (p. 55):

At 1st level, you acquire the training necessary to effectively arm yourself for battle. You gain proficiency with medium armor, shields, and martial weapons.

Can a Warlock with the War Caster feat (PHB, p. 170) use both staff (only for casting, never melee attacking) and a shield to increase AC?

And how to deal with staffs that give you extra AC, like the Staff of Power?

Staff, very rare (requires attunement by a sorcerer, warlock, or wizard)

This staff can be wielded as a magic quarterstaff that grants a +2 bonus to attack and damage rolls made with it. While holding it, you gain a +2 bonus to Armor Class, saving throws, and spell attack rolls.

Can a warlock with:

• Shield +1 [+3 AC]
• Staff of Power [+2 AC]
• Half Plate armor [AC 15 + Dex (max 2)]

Reach 15 + 2 + 2 + 3 = 22 flat AC, and have all the benefits given by the staff? (The shield spell would also temporarily boost this to 27 AC.)

Would this all work as I have described?

HexBlade Warlocks give you proficiency with shields:

Hex Warrior

At 1st level, you acquire the training necessary to effectively arm yourself for battle. You gain proficiency with medium armor, shields, and martial weapons.

Can a Warlock (with Warcaster feat) use both staff (only for casting, never melee attacking) and a shield to increase AC? and how to deal with staffs that gives you extra AC like Staff of Power

Staff of Power

DMG Staff, Major, Very Rare (Requires Attunement by a Sorcerer, Warlock, or Wizard) 4 lbs.

This staff can be wielded as a magic quarterstaff that grants a +2 bonus to attack and damage rolls made with it. While holding it, you gain a +2 bonus to Armor Class, saving throws, and spell attack rolls.

Can a warlock with

Shield +1 [+3 AC]

Staff of Power [+2 AC]

Half Plate Armor [AC 15 + Dex (max 2)]

Reach 15 + 2 + 2 + 3 == 22 flat AC? and have all the benefits given by the staff? (and he can still cast Shield spell to reach 27 AC)

HexBlade Warlocks give you proficiency with shields:

Hex Warrior

At 1st level, you acquire the training necessary to effectively arm yourself for battle. You gain proficiency with medium armor, shields, and martial weapons.

Can a Warlock (with Warcaster feat) use both staff (only for casting, never melee attacking) and a shield to increase AC? and how to deal with staffs that gives you extra AC like Staff of Power?

Staff of Power

DMG Staff, Major, Very Rare (Requires Attunement by a Sorcerer, Warlock, or Wizard) 4 lbs.

This staff can be wielded as a magic quarterstaff that grants a +2 bonus to attack and damage rolls made with it. While holding it, you gain a +2 bonus to Armor Class, saving throws, and spell attack rolls.

Can a warlock with

Shield +1 [+3 AC]

Staff of Power [+2 AC]

Half Plate Armor [AC 15 + Dex (max 2)]

Reach 15 + 2 + 2 + 3 == 22 flat AC? and have all the benefits given by the staff? (and he can still cast Shield spell to reach 27 AC)