The Great and Powerful Trixie does not require your permission to speak to her heart’s content about whatever subject tickles her fancy. But, since you are in such need of aid, The Great and Powerful Trixie supposes she can spare a moment from her busy schedule to indulge.

Hatching the Pokemon eggs is easily the most boring and time consuming part of Pokemon breeding. Simply carry five eggs at once, and a Pokemon with the Flame Body or Magma Armor ability. As you must always carry a Pokemon with you at all times, only a foal would waste their time hatching eggs without such an addition.

As each egg of the desired Pokemon hatches, if they do not possess the desired Nature/Ability, then release. By that time you will likely be able to acquire another egg and continue. As it is a continuous sequence, Trixie recommends you bicycle back and forth along the same route as the daycare to speed up the process of hatching, release, and procurement.

As far as leveling the newly hatched Pokemon, if you are in a rush, re-battling the Elite Four and Champion, along with attaining the maximum rank in the Battle Chateau will allow you to fight the highest level trainers available. Simply give the desired Pokemon the Lucky Egg and open every encounter with said Pokemon; switching them in and out as each opponent’s Pokemon is defeated.

However, The Great and Powerful Trixie must caution you. Always EV train your Pokemon first using your preferred method.

As for the remainder of your plebeian rambling, The Great and Powerful Trixie does not know of any Lyra or Bon-Bon. However were she, however unlikely it may be, somehow stricken down with physical injury, she would not oppose to being waited on in admiration by her adoring fans. Not that she isn’t already.