Your proposed AC calculation is incorrect, because you seem to have misunderstood a few different things.
Mage armor is totally incompatible with armor
The mage armor spell description says:
You touch a willing creature who isn't wearing armor, and a protective magical force surrounds it until the spell ends. The target's base AC becomes 13 + its Dexterity modifier. The spell ends if the target dons armor or if you dismiss the spell as an action.
This clearly states that you can't have mage armor active while you're wearing armor. If you're wearing armor, mage armor can not target you; if you cast the spell first, it ends as soon as you put on armor.
Furthermore, mage armor provides a new AC calculation method. This is important to note, because...
Multiple AC calculations don't stack (only bonuses to AC do)
The description of armor class in the rules states:
Without armor or a shield, your character’s AC equals 10 + his or her Dexterity modifier. If your character wears armor, carries a shield, or both, calculate your AC using the rules in the Equipment section. Record your AC on your character sheet.
Some spells and class features give you a different way to calculate your AC. If you have multiple features that give you different ways to calculate your AC, you choose which one to use.
This is reiterated at length in the Sage Advice Compendium:
How do you calculate a creature’s Armor Class (AC)?
Chapter 1 of the Player’s Handbook (p. 14) describes how to determine AC, yet AC calculations generate questions frequently. That fact isn’t too surprising, given the number of ways the game gives you to change your AC!
Here are some ways to calculate your base AC:
- Unarmored: 10 + your Dexterity modifier.
- Armored: Use the AC entry for the armor you’re wearing (see PH, 145). For example, in leather armor, you calculate your AC as 11 + your Dexterity modifier, and in chain mail, your AC is simply 16.
- Unarmored Defense (Barbarian): 10 + your Dexterity modifier + your Constitution modifier.
- Unarmored Defense (Monk): 10 + your Dexterity modifier + your Wisdom modifier.
- Draconic Resilience (Sorcerer): 13 + your Dexterity modifier.
- Natural Armor: 10 + your Dexterity modifier + your natural armor bonus. This is a calculation method typically used only by monsters and NPCs, although it is also relevant to a druid or another character who assumes a form that has natural armor.
These methods—along with any others that give you a formula for calculating your AC—are mutually exclusive; you can benefit from only one at a time. If you have access to more than one, you pick which one to use. For example, if you’re a sorcerer/monk, you can use either Unarmored Defense or Draconic Resilience, not both. Similarly, a druid/barbarian who transforms into a beast form that has natural armor can use either the beast’s natural armor or Unarmored Defense (you aren’t considered to be wearing armor with natural armor).
What about a shield? A shield increases your AC by 2 while you use it. For example, if you’re unarmored and use a shield, your AC is 12 + your Dexterity modifier. Keep in mind that some AC calculations, such as a monk’s Unarmored Defense, prohibit the use of a shield.
Once you have your base AC, it can be temporarily modified by situational bonuses and penalties. For instance, having half cover gives you a +2 bonus to your AC, and three-quarters cover gives a +5 bonus. Spells sometimes modify AC as well. Shield of faith, for example, grants a target a +2 bonus to AC until the spell ends.
Magic items can also enhance your AC. Here are a few examples: +1 chain mail gives you an AC of 17, a ring of protection gives you a +1 bonus to AC no matter what you’re wearing, and bracers of defense grant you a +2 bonus to AC if you’re not wearing armor or using a shield.
In short: different AC calculations don't stack. If you have multiple ways to calculate your AC (e.g. Unarmored Defense, Draconic Resilience, Natural Armor, mage armor, etc.), you choose which one you want to use - presumably you'd choose the one that gives you the highest base AC.
What this means is that even if mage armor could apply while wearing armor, you couldn't calculate your AC by taking your regular AC calculation while armored (or unarmored) and adding your Dex modifier again from mage armor.
Mage armor gives you an AC calculation method of 13 + Dex mod. The fact that your Dex mod is +3 is just an odd coincidence; if your Dex mod was +0, mage armor would still give you an AC of 13 (before considering any AC bonuses).
Moving on to AC bonuses...
The Defense fighting style requires armor
The Defense fighting style option states:
While you are wearing armor, you gain a +1 bonus to AC.
It requires you to be wearing armor to gain its benefit. This means you can never get this bonus on top of mage armor, because they're mutually exclusive.
Bladesong works, as long as you're not wearing medium/heavy armor or a shield
The Bladesinging wizard's Bladesong feature (SCAG, p. 142) says:
Starting at 2nd level, you can invoke a secret elven magic called the Bladesong, provided that you aren’t wearing medium or heavy armor or using a shield. [...]
You can use a bonus action to start the Bladesong, which lasts for 1 minute. It ends early if you are incapacitated, if you don medium or heavy armor or a shield, or if you use two hands to make an attack with a weapon. [...]
While your Bladesong is active, you gain the following benefits:
You can use this feature twice. You regain all expended uses of it when you finish a short or long rest.
This grants you a temporary bonus to your AC equal to your Int mod, and can be used either when unarmored or when wearing light armor (as long as you're not wielding a shield). Because this is a bonus to your AC, not a new calculation, this does stack with whatever base AC calculation method you use.
Final AC calculation
If you're unarmored, have mage armor active on yourself, and start your Bladesong, your total AC while Bladesong is active would be:
13 + 3 (from mage armor)
= 16 base AC
+ 3 Int (from Bladesong)
= 19 total AC (while Bladesong is active)
Even if you multiclassed into fighter, ranger, or paladin and chose the Defense fighting style, it would be incompatible with mage armor. You could only benefit from the Defense fighting style while wearing armor, which would give you a different AC calculation (the exact calculation depends on the armor you wear). And if you chose to wear medium or even heavy armor or equip a shield (even if you were proficient), you would be unable to get the AC bonus or other benefits from Bladesong.