[RPG] Can a Battle Smith artificer change the appearance of a Steel Defender after creating it

By default, artificers are capable of making magic items in three main ways. Certain subclasses gain additional methods for making specific magic items (e.g. the Artillerist gains the ability to make a specific variety of magic wands with their Wand Prototype class feature) detailed in their class features, but these are applicable to all Artificers:

First, they can simply use the explanation of "I created a temporary magic item" as an explanation for how they cast a spell with a Tool as their Arcane Focus. For instance, casting Cure Wounds with an Alchemist's Tool could be explained as creating a temporary healing potion and immediately feeding it to someone before the magic on it wears off. The explanation for this is found in the "The Magic of Artifice" sidebar in the 2019 Artificer Unearthed Arcana articles.

Second, they are capable of creating temporary magic items using their Infuse Item class feature. This works in accordance with the rules of that feature, with them only knowing a set number of Infusions for their level, only being able to create one item for any given Infusion at a time, and only being able to create a set number of magic items with that class feature at a time. The rules for this are explained in the relevant class feature in the 2019 Artificer UAs.

Third, they are capable of creating permanent magic items using the rules for the Crafting A Magic Item downtime activity in the Dungeon Master's Guide and Xanathar's Guide to Everything. This allows them to create magic items that, by default, are limited to magic items listed in the relevant sections of the Dungeon Master's Guide and other published books.

This is the mode where possessing formulas for the magic items is required; there are no rules for the acquisition of these, so it largely falls into the realm of DM fiat - the PCs might be able to create them themselves (possibly with a non-magical item crafting check), they might need to go on adventure to find one, they might find them as treasure while on adventures for other reasons, or, if you simply don't want a PC to be able to craft a certain item, you can simply say that PCs aren't able to find the formula they want. Effectively, they allow you, as a GM, to filter what items you want to allow PCs to craft.

If you wish to allow them to create homebrewed magic items with the last option, you would simply assign the item a Rarity based on your evaluation of its power level and then he would simply follow the rules for creating an item of that Rarity level. For the specific items you're mentioning, there are two published magic items that are broadly analogous to the items your player wants to make: for the first, there is the Boros Guild Signet from Guildmaster's Guide to Ravnica, and for the second, there are the Boots of Striding and Springing from the Dungeon Master's Guide.

Yes. Your steel defender can attack, so long as it's acting independently.

From the Controlling a Mount entry..

An independent mount retains its place in the initiative order. Bearing a rider puts no restrictions on the actions the mount can take, and it moves and acts as it wishes.

And then from the Steel Defender entry, it reads..

It is friendly to you and your companions, and it obeys your commands. .. It can move and use its reaction on its own, but the only action it takes on its turn is the Dodge action, unless you take a bonus action on your turn to command it.."

Given this, when your steel defender is acting independently, it's obeying your commands. There is no indication that commanding your steel defender and controlling your mount are the same thing.

You can control a mount only if it has been trained to accept a rider. Domesticated horses, donkeys, and similar creatures are assumed to have such training. The initiative of a controlled mount changes to match yours when you mount it.

And here is why. A steel defender hasn't been trained to know that you want it to go faster when you kick its sides, or that you want it to right or left by pulling on the reigns. The steel defender just obeys your commands, which is separate and distinct from controlling a mount.

There is also no mechanical benefit to controlling it; its initiative is already the same as yours, and it already moves as you direct you, and those are the only benefits of controlling a mount. Controlling it would only limit the actions it could take.

I heavily edited my original post because, after thinking about it, I was kind of all over the place and wanted to give a more concise, sensible answer.