No. The runner still has the same mass, so accelerating takes the same amount of energy as 1x gravity. It's like shifting to a higher gear on your bike.
Not exactly. Horizontal acceleration takes the same amount of energy. The mass of the body must also be supported upon landing, which obviously takes more energy with more gravity.
Interesting. So it will feel like your normal weight in the horizontal dimension, but it will feel like wearing a 100-pound backpack in the vertical dimension.
Your ultimate running speed then depends on how strong you are. That 100 pound "backpack" will push you into the ground and give you far more acceleration than your normal weight would allow: it will feel like you have ultra-traction. But when you push to the side and accelerate your body, you're only accelerating your normal body weight.
Marathon times will likely suffer, but perhaps some short sprints will be faster in gravity over 1g.