How can those not be coincidences? They are blantant coincidences. Not everyone gets a random piano student (who happens to be the rivals sister!) nor gets confessed to by an upperclassman. And those happened with perfect timing too. And everyone seems to be at Kousei's first recital!

That's just what drama is. Stupidity and nonsensical secrecy is also part of the genre, like how the lie in Shigatsu could've been explained from the beginning, or how ridiculous it was for Kousei's mother to keep her motives secret from her child. It's unfair to judge this show differently. The execution was just so much better in Shigatsu, but the core believability of everything is not so different.

Now I'll try to explain a bit about those logical flaws you mentioned.

1) Tsukasa is an idiot. Done.
2) Giftias need to be recovered. Their section is endangering human lives by taking extra time to retrieve Giftias. Of course they're a liability. Companies are also concerned with money, and spending extra time to do the same thing other sections do is just bad performance.
3) Danger to humanity -
It wasn't designed to be like that. It's a side effect that they can't fix, and an accepted one. Why is it accepted? Because it shouldn't really happen unless the human owner abuses (does not return it in time) the Giftia. Like any tool, it depends on the user. A gun, a knife, or even a pen can be just as dangerous when not used properly. This links back to item number 2. Dallying when retreiving Giftias is a no-no, thus their section sucks in the eyes of the brass.

Another reason why this risk is accepted is because Giftias are just that awesome. See Isla.