The undead don't start there, silly.

Well, water-based latex will not stick to oil based anything. It will go up and look like it's working. But it won't attached to it. Sherwin Williams has a primer called quick dry that is also stain blocking or even their extreme blocking primer. They're pricier if you're not a contractor. Know one? Ask them if you can use their account.

There should not be an oil base on the wood paneling. If there is, the kilz wouldn't have stuck to it bc latex and oil don't play well since latex is water based. Can you peel the kilz off? If so. Then you'll have a problem. If that's the case, you'll need to get a hybrid primer that plays with both, after you strip your kilz off.

If it doesn't. You're in luck! Get a primer ment to block the bleed through like the person prior recommended and paint away. I'd recommend a gray primer if going dark on your latex color.

Pilot holes and wood screws, probably 1" should suffice. If you're mounting directly to the window frame like that.

In sheet rock, pilot hole, self tapping drywall anchors and the screws they came with. Somewhere in between a machine and sheetrock screw.