I really don't see the difference between this a dragonborn and a red abishai

Using the rules in the DMG, the challenge rating for this creature is nowhere near 7. According to my calculations it stays at 3 

The DC for the breath weapon should be 12.

The proficiency bonus should be +2

The weapon attack bonuses are correct, though at +5

this is litterly a dragonborn

What does the part about size and breath weapon at the end mean? Why would a half-dragon's size be anything but medium, the size assigned to it at the beginning of the stat block?

Have you calculated both the defensive and offensive capacities? The breath weapon usually does so much damage to change it's offensive Cr significantly Along with it's fire resistance changing how they calculate the hit points making it's Cr raise while having low hot points. I haven't calculated it out yet but that changes things

It can be other sizes, because the half dragon stats are a template that can be applied to beasts, giants, or monstrosities, not just humanoids. So for most, if not all, humanoids, that’d fall under “Large or smaller”

 But a Half-Dragon Elephant would be huge, and use the breath weapon of a young dragon instead of a wyrmling.

Also, because their creature type does not change, a Druid could wild shape into a half dragon beast, as long as they met the CR and flight/swim requirements

Find it funny people just assume dragons True Polymorph into humans to make half-dragons and not spellcasters True Polymophed into dragons XD

Use the Half Dragon Template information.

Dragonborn are humans that were magically altered into draconic beings, they share no blood with actual dragons however. 

Half Dragons are the offspring of shapeshifted dragons and other creatures, and thus are directly related to dragons.

"Multiattack. The veteran makes two longsword attacks. If it has a shortsword drawn, it can also make a shortsword attack."

Does this mean it is two weapon fighting, and just ignoring the use of a bonus action to do so? 

nah

I do not think it ignores the bonus action requirement of two weapon fighting it just does not list it because it has no other bonus actions it can take at least not that I can think of 

npc do not follow pc rules

Thanks, that makes sense. 

It helps me run them, sometimes. 

Does a metallic half dragon gain both breath attack of the dragon parent? Or just one?

Does a gem half dragon gain both resistances?? Or just one?

Quote from Layomayo >>

Does a gem half dragon gain both resistances?? Or just one?

 Per these rules, the are no Gem half-dragons, but that is probably because this came out before Fizban's.  For both of your questions, I would rule either they have only one to keep things simple, or both & figure out what chromatics get to keep things balanced. Chromatic Warding from Fizban's?

A Dragonborn isn't really born from a dragon. A Dragonborn is made from a dragon kind of just making one, at least I think. And a half-dragon is when a dragon and anything else mates. In this case it's a dragon mating with a humanoid creature.

ahem, how did this happen?