As for how the contests work, this is how things will go:
Hoenn
Standard appeal: (anime style – coordinators have their Pokemon use moves to appeal to the four judges). Essentially, role players who can write descriptively will likely have an edge here, because they will probably be able to paint the best 'picture' of how their Pokemon are manouvering. However, like in the anime, elegance/beauty/image isn't everything. If a coordinator can hype up the audience and interact well with them to garner a good response, this also qualifies as a success!
Battle Round: Battles last five minutes. There is a short health bar for each trainer, and depending on certain slip ups (a Pokemon being trapped by psychic, taking hits, something failing like attempting a sleep move during uproar) the health bar will decrease. Whoever's Pokemon is knocked out first, or whoever has the least health when the time is up, is declared the loser.
The final rounds of the Grand Festival will be under 'Double Performance' ruling. A trainer will use a single Pokemon during the appeal stage and battle with two Pokemon. One of these Pokemon can be the same as the appeal.
Sinnoh
Standard Appeal for first round.
Second round: Dance round. A genre of music will be played with the Pokemon attempting to dance with it. Again, good writing skill with probably help here. The success/amount of points gained will be RNG dependent (IE – how many beats the Pokemon won and missed. A step can be counted as 'good' for one point or 'excellent' for two or simply be a 'miss'. There are sixteen beats to count.) A Pokemon will have two chances to be a centre dancer, and also as a back dancer.
Hearthome City and the Grand Festival are conducted under Double Performance ruling, including for the appeal rounds. Trainers are encouraged to dress up, and it will be taken into account if they coordinate this with their Pokemon or a theme during the appeal round.
Kanto follows Hoenn's contest rulings.
Trainers won't be charged for purchasing seals, however if a Pokemon is contained in a special ball (for example a Luxury Ball, Friend Ball, Net Ball, etc), this may be taken into account if it adds anything to the appeal, and same if the seals work for the routine as well.
That's all you need to know, i believe. If you have any questions, feel free to ask!