I have full plate armor (18 AC)

I have a +2 shield (+4 AC)

I am a 5th level Fighter with defensive fighting style (+1 AC)

I am a 6th level Cleric of the Forge which grants me

- Blessings of the Forge: I gain the ability to imbue magic into a weapon or armor. It becomes a magic item granting a +1 bonus to AC if it's armor (+1 AC)

- Soul of the Forge: My mastery of the forge grants me special abilities. While wearing heavy armor, I gain a +1 bonus to AC. (+1 AC)

Your calculations are correct, as far as I can see.

For theorycrafting purposes, you can increase this a little more with a ring of protection or a cloak of protection, or, obviously, getting a better than +1 armor. Perhaps a Defender too? :p

Just keep in mind that even a goblin can still hit you on a roll of 20 (and for double damage, too), so don't get too comfortable.

And while 5th edition rules mean your magic items are safe from a Rust Monster, be wary of Heat Metal - it's a lot of damage for its level with no actual save.

Yes. Bonuses always stack unless they're from two game elements with the same name.

Can you tell me where you read that rule in 5e please?

Check out 'Combining Magical Effects' in the Player’s Handbook, p. 205.

Also, this Sage Advice column, specifically: 'A bonus always gets added when the game instructs you to add it, unless you’re already receiving the bonus from a game feature with same name.'

The relevant rule comes from the DMG errata.

Chapter 8 Combining Game Effects (p. 252). This is a new subsection at the end of the “Combat” section:

Different game features can affect a target at the same time. But when two or more game features have the same name, only the effects of one of them—the most potent one—apply while the durations of the effects overlap. For example, if a target is ignited by a fire elemental’s Fire Form trait, the ongoing fire damage doesn’t increase if the burning target is subjected to that trait again. Game features include spells, class features, feats, racial traits, monster abilities, and magic items. See the related rule in the “Combining Magical Effects” section of chapter 10 in the Player’s Handbook.

This is repeated in the intro to Xanathar's Guide to Everything under "Ten Rules to Remember":

Combining Different Effects

Different game effects can affect a target at the same time. For example, two different benefits can give you a bonus to your Armor Class. But when two or more effects have the same proper name, only one of them (the most powerful one if their benefits aren’t identical) applies while the durations of the effects overlap.