I didn't know there was a functionality to drop them in flight? Could you drop the rocket pod in flight too once it's empty?
Yes, you can, but as an emergency. You can drop anything from pylons - up to and including, say, sensor pods.
As with many things - you (as a pilot)
better not to in peacetime. Because you guess who's going to pay for the replacement.
As for rocket pods - for some older rocket pods, it is even their intended way of operation (FFARs had single-use pods, for example).
The article is worded at some points as if the planes are that much of a game changer.
Well, they intend to get ~220 of them overall. That's a pretty big force by modern standards.
As for a "game-changer" - this word is horrifically over abused. Very few things can be "game changers" when your main adversary is a superpower. F-16V, with all its useful tricks and technological sophistication, isn't one of them.
Took them long enough. Wasn't this signed when Obama was still POTUS?
Their small tragedy is that there is a perfect fighter solution for ROCAF on the market - a far cheaper one, in fact. That's Gripen E/Globaleye pair.
Aaand they absolutely couldn't buy it.