Day care is not considered child support.
If the daycare is for the father's child, yes, at least half of the daycare depending on father's income versus ex's income. If the daycare is for the ex's child by another father, no.
You can breed it at the daycare.
daycare, creche
Not a traditional one-Daycare is though.
No. You can only run a daycare in the Sims; you cannot drop your children off at another daycare.
no
put it in daycare with another serperior or a ditto any level
put a ditto in the daycare with another Pokemon
Not legally. It would be considered to be discrimination.
You have to trade a daycare egg and trade it with another person that has a Togipi egg
Put in a ditto and lucario in the daycare.
pretty much nothing besides leave it in the daycare with another Pokemon to have them breed