How flat does a runway need to be?
As an anecdotal answer to your first two questions, paved runways used by air carriers that have obviously noticeable vertical curves are a minority but not uncommon.

Unless they've redone the runway at Stansted, north of London, there's a significant hump in the middle. I used to operate through it at night in the early 1990s. As a bit of fun, we'd arrange legs so that a new first officer would have the leg into Stansted. On final at night the hump was not noticeable. However, when you touched down, the runway lights along the last half of the runway would disappear, at which point the captain would observe, "Hmm, not much runway left."

If you define a runway simply as a strip of land regularly used by aircraft, there's a whole lot of them that have vertical curves, and many with horizontal bends as well. It's gone now, but there used to be a strip at a lumber mill in North Fork, California, that had a 10-15 degree bend in the middle. McKenzie Bridge airfield just upriver from my home in Oregon has a steep incline on the east end.

Landings and takeoff on uneven runways are not significantly more complex than on straight runways. If the runway qualifies as an uphill/downhill runway, you generally takeoff downhill and land uphill. Touching down on the downside of a hump can make your landing feel a little softer than otherwise. Touching down on the upside of a hump makes it a little harder than otherwise.

Accommodating a horizontal curve is more challenging. It's worth remembering, though, that seaplanes often use a curved takeoff run.