I believe that as sensor increases, the DOF will decrease for a given aperture. Aperture is a variable opening in which light enters a camera. I'm not really sure about defocus blur as the concept of defocus blur isn't as clear to me. Off general intuition, I believe that increasing sensor size will probably increase defocus blur.
As the sensor size gets bigger, we need larger lenses to emulate the same focal length. So an 85mm equivalent lens on a 35mm camera sensor would be much wider on a full frame sensor. As such, the focal length actually needs to be increased on the full frame sensor. Because the lens is much larger now (even though the equivalent focal length is the same) we get much more blur. So in this sense, I suppose it isn't really connected to sensor size but rather just focal length. If my understanding is correct.
To this end, it might as well be tied to sensor size since its one of the only ways you can get more depth of field and defocus blurring if you have already maxed out everything else. One of the reasons photographers or videographers may or may not choose a wider sensor.
For a given lens and f-stop, moving closer to the subject (while adjusting focus onto the subject) would result in a narrower DOF, making further objects be less focused. The reverse is also true - moving further from the subject would result in a wider DOF and cause further objects to be more in focus.
Generally, focal length affects DOF significantly. Increasing focal length will result in a narrower DOF, while shorter focal lengths will result in a wider DOF.
1:1 macro means the image on the camera sensor is the same size as the actual object. So yes, achieving a sufficient depth of field can be challenging due to the close distance between the lens and the subject, as well as the typically narrow aperture used to maintain sharpness.