Ellipse, circle, parabola, hyperbola - all so called conic sections - are orbital trajectories; when you entering the atmosphere (which means you're technically not on a strictly circular orbit), you're initially following the part of that curve which is closest to the planet.

The curve is such that if you don't lose enough speed, you're going to start moving way from the planet.

If you're still on parabola (technically you never are, it's infinitely thin case between ellipse and hyperbola, physically not really possible) or hyperbola, you're not comping back - so if you need to get to the planet, you have to be on elliptical trajectory.

Even if you're on ellipse, you don't want that ellipse to be too elongated - e.g. the elliptical trajectory from the Earth to the Moon, which is rather close to parabolic one, takes about 4 days one way. You don't want to spend that much time when you're landing, so you need to lose enough of speed in the atmosphere. Which means you need to brake relatively aggressively.

This means there's a "reentry corridor" - not too steep, not too shallow, and the spacecraft needs to survive the reentry, and going from the Moon is harder than going from LEO because coming from the Moon the spacecraft has higher initial speed entering the atmosphere. It's still possible to balance various approaches, but you can't have (correction: it must be particularly hard to have...) zero fuel use, relatively fast landing (without long ellipses between reentries), speedy planet approach and low heating at the same time.

It's hard to do that. What you suggest would mean losing all your orbital speed before you hit the thicker layers of the atmosphere. You could probably do that, but you'd use a lot of fuel to decelerate. And then you are still being accelerated downwards by gravity, so you need something to counter that, which means you need to burn fuel all the way down. All that fuel adds a lot of weight, which cuts down on the amount of useful stuff you can take with you.