Does everyone's eyes have to adjust to new glasses?

Not necessarily. People who need glasses to see properly often see great immediately. If the glasses are too weak or strong, do not sit at the right position, are tilted, or have their "sweet spot" off center, there can be difficulty getting used to them. In these cases, the glasses need to be adjusted. If you never wore glasses or there is a big change in prescription, it may take some time to adjust to them.
Usually yes. With a new pair of glasses, the power of the lenses may be stronger, and the frame is often different so the size (diameter) of the lenses is also different from the old lenses. Thus, the image seen through the new glasses is a bit different (sharper, and with different edge distortions), and the brain needs a day or two to adjust. After a couple of days, the view will seem "normal" to the brain.