A "manuever" is a difficult set of movements made to accomplish a goal. "Tying their shoelaces is a difficult maneuver for a child." "It was a bad road. It was full of bumps and holes. He had to maneuver the truck carefully."

The air has resistance. If something moves through the air, the air resists it. It pushes back. Something trying to push through the air is held back by the air dragging on it. In aerodynamics, this force is called "drag." He says that a parachute that size will have enough drag to slow a falling object by 20%. "He started down the corridor again" means he began to walk again. They were walking together. They stopped walking to watch and talk. They were standing still. Kohler began walking again. He started to walk. They were in a corridor. "Down the corridor" is a vague indication of direction. You walk "down" a corridor until you open a door and turn into a room. We could say "Kohler started to walk down the corridor again." We know what he stopped doing--walking. So we can just leave out "to walk" and say "he started down the corridor again.

A "swathe" is a broad piece of fabric. A piece of fabric, like the sail of a boat, may flutter and wave in the wind. Then it catches the wind. It fills with air. It becomes tight and smooth. That is "billowing."

The "diameter" of something, especially something circular, is the distance across it. A coin has a diameter of one or two centimeters. A dinner plate has a diameter of about thirty centimeters. A "yard" is a traditional unit of length in some English-speaking countries. It is exactly 91.44 centimeters. Usually, you can just think of "a yard" as "a meter." Her parachute has a diameter of about a yard, or about a meter, about the same as a large umbrella.

"Maneuver" in this case means to move around making one's way to the window but either has difficulty or has obstacles in the way to get there. The fact that the sentence indicates she's overweight (obese) tells me that she didn't exactly walk straight to the window, but it took some effort. She either had to walk around things or walk slow and steady over things to get there. "Swathe" means she is wrapped in a garment or has something very freely draped over her, think of a kaftan or tunic. Something not fitting to her body, but freely wrapped or draped. "Billow" means that it's flowing (from the air). Think of a light-fabric that freely breezes around as the person walks. "Like a toy" means her garment shouldn't be taken seriously. It's amusing to see it. "One square yard of drag" is a physics reference. If you look up "drag in physics" in Google, you will see that it has to do with force or resistance to acting opposite to the relative motion of any object moving with respect to a surrounding fluid". Link: https://en.wikipedia.org/wiki/Drag_(physics) (In English, we don't usually go around using the word "drag" like this. Brainy people or scientists might use this word more, but for people like me, I had to look it up to get the meaning of it. Once I had it, I understood it, but I would have worded it in a more simple way.)