Short answer, no.
Ancestral Arms is an alternate racial trait, which isn't the same kind of "trait" as the thing normally called a "trait". Alternate racial traits operate under different rules, and they can't be taken unless you are that race.
Heirloom Weapon specifies it must be either a simple or martial weapon.
However, perhaps you can work something out with your GM.
Well, as a fighter you can get exotic weapon proficiency at level 1 anyway. Your backstory can of course be a valid reason for having it, but I'm not sure you'd want to use the rules like that to make it seem more official. You'd get the same effect with a normal EWP, and it is best to go simpler.
This does bring up a good question though: would it be racial heritage half elf or racial heritage elf? While people treat half elves as their own race, since it is thinned out like this, you are a more human with some degree of elf blood.
Not sure how useful heirloom weapon is though. You'd end up with problems if it ever got stolen, broken, eaten by a rust monster. Plus, while I am sure there is some spell or something that would make it masterwork, it would just be more trouble than simply buying a masterwork weapon when it comes time to enchant them. Using the trait along with EWP would likely give you a small boost that could help you survive early levels though.
Humans can trade their free feat for the weapon training of any race. So you could pick up eleven weapon training, orc, or even the tengu one.
Actually, the weapon training might be a better option than EWP. As a fighter, it doesn't give you any new weapons other than the elven curved blade, but it also a language that helps flesh out your character (you will not likely have a high enough intellect for extra languages or skill points for linguistics unless you are a lore warden..which you might want anyway since it seems better for someone descended from elves flavor wise I suppose). Either way, you'd be burning up a feat, so get the most out of it I guess.
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This is easy.
Exotic Weapon Proficiency(Elven Curve Blade) feat, and the Adopted trait to gain a Elf race trait(I suggest Warrior of Old).
If you want to take Elf-only feats or archetypes, then Racial Heritage(Elf) will allow you to do so.
If you are not going to take either, then the one trait and feat should be all you need.
Flavor as appropriate.
The Adoptive Parentage under alternate racial traits give you weapon training if the chosen race has it (weapon focus or skill focus otherwise)
There is a trait (forgot thr name) that gives you a nonharmful cantrip 3/day, so it does what you want from arcane talent but for a trait instead of a feat.
And the only big game hunter I found is a feat not a trait