Okay, Onii-chan brought this upon himself be rewarding bad behavior.
Instead of accepting her unconditionally, he created a situation where the price for his love is her being willing to pay the ultimate price if she doesn't get it. And now she knows that she can use that as leverage.
Guys, if you don't want a yandere imouto, you need to keep her in permanent ~dere mode. It's by being half-assed in loving her that she'll find your weakness and use it to manipulate you.
The "I'll kill myself if you don't X" troupe gets old too quickly, so this better be the opening for something else.
Yes. The opening for him doing whatever she wants to avoid letting her issue that threat again.
He neglected her earlier and now that she has reached her limit, he has given up all control over this relationship. If he loved her properly from the beginning, she'd never have reached this extreme and would likely have been happy to move at his pace.