Buying Hairlooms for difference Faction character

Is it possible to my Horde 80 character to buy Hairlooms for my alliance low level chracter ?

You can create horde alt, give it heirlooms. After you make faction change on site and make it alliance character. Done.

You should be able to mail them to the opposing faction.

Heirlooms are cross-faction. You can send them between Alliance and Horde freely. And no, you can't send gold or other items with the mails.

Thanks you

There are some you can only transfer with faction change, like pvp medallion.

You can also buy Wintergrasp Commendations to transfer honor to other characters, although the level 60 trinket you can buy with honor does not have resilience unlike the heirloom.