No, with an asterisk
First, look at the description from Xanathar's:
To start with, a character needs a formula for a magic item in order to create it. The formula is like a recipe. It lists the materials needed and steps required to make the item.
An item invariably requires an exotic material to complete it. This material can range from the skin of a yeti to a vial of water taken from a whirlpool on the Elemental Plane of Water. [...] The Magic Item Ingredients table suggests the challenge rating of a creature that the characters need to face to acquire the materials for an item. [...] In addition to facing a specific creature, creating an item comes with a gold piece cost covering other materials, tools, and so on, based on the item’s rarity.
Now look at the Artificer's Replicate Magic Item Infusion:
Using this infusion, you replicate a particular magic item. You can learn this infusion multiple times; each time you do so, choose a magic item that you can make with it, picking from the Replicable Items tables. [...] See the item’s description in the Dungeon Master’s Guide for more information about it, including the type of object required for its making.
It just refers back to the DMG so it doesn't give us any hints.
Nothing in the DMG description ever mentions the casting of a spell, so we cannot be sure that spell casting is even a requirement (likely, but not guaranteed). Completely up to the DM.
The whole Infusion process is just a "touch".
You also brought up enhancing their other Infusions. That's still a no because...
Whenever you finish a long rest, you can touch a non-magical object and imbue it with one of your artificer infusions, turning it into a magic item.
Touch, not "Cast a spell".
Metamagic is a one-time buff
If we look at it from the Sorcerer side...
You can use only one Metamagic option on a spell when you cast it, unless otherwise noted.
Metamagic can only be applied (except where noted) when the Artificer casts a spell. So even if the DM decided that a spell was cast during the creation, the Metamagic only works when you cast it. It would have no effect on future castings of the spell via an item.
None of the Artificer Infusion (Other than Replicate Magical Item) casts a spell, although they can have magical effects. The Armorer pieces also do not casts spells, they just do non-standard damage (thunder and lightning).
So the only piece left is casting a spell through a magic item which is answered nicely here.
Long story short, you can use the Metamagic feature if using an item that allows the Artificer to cast a spell. But it has nothing to do with being an Artificer.