pokemon-seriespokemon-sixth-generation
Someone on a trading group offered me an 'Event Pikachu', which was a Pikachu that knows Surf (normally impossible to teach to Pikachu).
Unfortunately it was a previous Generation's Event, and as such doesn't count as a 'Kalos-Born' Pokemon for tournaments/rating battles and the like.
So assuming I got a hold of it, could I breed this Pikachu to get a Kalos-born Pikachu with Surf?
Yes, as long as you have one parent that knows a passable move to the offspring, you will be able to pass an egg move.
It doesn't matter whether that egg move itself was obtained via breeding; a move is a move and it can be passed if it can be passed on.
As of Gen VI, it doesn't matter whether this egg move is on the father or the mother Pokémon. As long as any one has the eggmove, it can be passed down (breeding was made easier in more than one way in Gen VI!).
Sources:
Does having both parent Pokémon, of the same species and with Hidden Abilities, increase the chances of getting a baby Pokémon that has said Hidden Abilities?
No. Whilst both Male and Female Pokémon have a chance to pass on their Hidden ability in Gen 6, Male Pokemon will only have this chance to pass it on when breeding with Ditto. When breeding with the same species, only the Female's Hidden Ability matters.
Is having a gender specific Pokémon a deciding factor if the egg would be a male or female variant?
No, each Pokemon type has a specific ratio to be a specific Gender. The most common is a 50/50 chance to be either Gender (which your Ralts has):
There are also Pokemon that have more skewed results toward a specific gender. Eevee for example, has an 87.5% chance to be Male. There are also Pokemon that are always one Gender like Kangaskhan, and Pokemon that are Genderless, like Metagross. (These must be bred with Ditto, they cannot reproduce with a member of the same species).
You should have a look at Bulbapedia's Breeding Guide, as it covers a lot of ground about Egg groups, getting Egg Moves, Hidden Abilities, IVs and other useful info.
Best Answer
It is not possible to get Surfing or Flying Pikachu in Generation 6 games, because Pokémon that know HM moves cannot pass through transfer systems.
Consequently, if someone is offering you such a Pikachu in X and Y, you can be pretty sure it's hacked - at least, until an event is run distributing it!
EDIT: Upon a little more investigation, even if a Surfing Pikachu event is released, breeding it will NOT give another Surfing Pikachu, because Pikachu is not compatible with the Surf HM and it therefore will not be passed down - only TMs that can be learned by the child (in this case, Pichu or Pikachu as the case may be) are passed.