I like the game so far. There is ways to get rare Youkai's and what not but you can only draw them 3 per day. Either with special coins or Play Coins. You can still get other Youkais but normal ones. The story is alright, pretty much follows the anime but with a lot of other quests and stuff to do. The battle is simple and short, not as long as Pokemon, so the feeling of grinding isn't there, which is awesome. I can see why this game is so popular in Japan, but mostly for kids la. It's still fun for adults but do not expect something hardcore. It's somewhat like Pokemon, where you collect all the Youkai there is, battle, and advance the story. I like it, but I'm not sure if a lot will. Look into some gameplay videos to decide. Demo does not do the game justice, the demo is crap and doesn't represent the game experience. So far I'm enjoying the game. I'd say 7.5/10 for now for a premilinary score until I can actually finish it
There is streetpass for getting Youkai.
Online multiplayer for battle only on the 2nd one, mostly just singleplayer.

Not sure what you want. But if you're expecting Pokemon, you'd better play Pokemon instead.
Many articles point this out already, and everyone is expecting the battle system to be something like Pokemon which is not.
It's a different game, and battle doesn't last that long except for bosses.  There are more mechanism in the game besides using powers.
Your Youkai gets possessed and starts being lazy for example, and you have to undo the curse, besides just fighting and fighting.
The auto attack is fine, that what makes it less grindy, and more enjoyable than Pokemon.
There are other mechanism that's not about fighting as well which is fun to play. Don't wanna spoil what it is, but if you get it you'll find out.
Story mission to advance through the story, as well as many side mission to easily level up your Youkai is nice.
Side mission also not about battling Youkai only, it can be about other stuff too. Like finding something, or solving some stuff.

Demo is shit, and no one should even play it, in an attempt to buy the game. Too little stuff or mechanism shown which makes it look boring.
While the real game has a lot more stuff to offer, besides just waiting for your Youkai Powers to activate.
In the demo you get to play common Youkai's only, while in the real game you can get rare Youkai's and higher ranked ones that is cool.
I also wonder why Japan likes it so much, playing the demo. But I just bought it anyway, and it's pretty good so far.
They already on their 3rd installment in Japan and still going strong. First doesn't seems to have online battles, but 2nd does.

Stay away from this game if you're expecting it to be like Pokemon, I wouldn't recommend it 
But if you don't mind looking for something different and trying something new give it a go.
Game is much more appealing to me than Pokemon, just something fresh and new.

Battle are simpler and less grindy.
At least for the first game, it's more focused on the story, side quest and collecting Youkai.
It's a kids game, but I'm enjoying it at the moment 

I also enjoyed that LBX game too, same game design, but this one has a good battle mechanism, maybe you can check LBX instead.