Yes. The Masuda Method still works in this generation and with Ditto(s/es). In fact, you don't even have to use a Japanese Ditto. So long as one of the Pokemon is from a different region than the other, then they have an increased chance of breeding a shiny Pokemon.
Since you say that you're going to evolve Eevee into Sylveon, let's look at Sylveon in particular:
Sylveon has a base Speed of 60. Unfortunately, this means that Sylveon falls well below the average base Speed of most Pokemon. This contrast is well illustrated by comparing Sylveon to Eevee's other evolutions, such as Jolteon's base speed of 130 (the fastest of Eevee's evolutions) and Umbreon's base Speed of 65. In fact, Sylveon has the lowest base Speed of all of Eevee's evolutions.
This means that if you choose Charm, you will most likely go after your opponent. Therefore, your opponent will have one turn to attack with their full power, after which Charm will lower their Attack by two stages, or 50% power. So, if Sylveon can take that initial full power hit, Charm is preferable. Unfortunately, Sylveon specializes in absorbing special-type attacks, not physical. Her base Defense, sitting at 65, is half of her incredible base 130 Special Defense.
Therefore, Sylveon won't be able to tank full-powered physical moves very easily. This is where Baby-Doll Eyes' priority comes into play. Sylveon is much more likely to survive 2/3-powered physical hit as opposed to a full-powered move.
Best Answer
The gender will be of normal Eevee distribution, which is to say 87.5% male, 12.5% female.