[Do you want to play?]

35 minutes ago, Fernan100tifiko said:

I am a rookie (Lv. 70), I would like to try a battle with someone else who fights like me. 

Sure, I'd be down. Send a battle request.

[Any way to free the daycare pokemon outside of shards?]

It's worth to buy all of them, yeah. Not only will you eventually get something worth, but shards are pretty easy to get later on in the game.