PNG images shouldn't lose any detail compared with TIFF images (both are lossless), but Xway's image scaling is probably better than Freeway's.
If you set the width or height to be half the natural width/height, then yes - this will double the resolution. On a low-resolution screen, an image that has 600x600 image pixels will be scaled down to half its size if it is placed within a 300x300-pixel box, but will be displayed at its natural resolution on a high-resolution (2x) screen. This means that the 600x600 image will look much better on a high-resolution screen than a 300x300 image (which would have to be scaled up for the high-resolution screen). The 600x600 image will also look good on a low-resolution screen: scaling down preserves much of the detail from the original image, but scaling up is unable to create extra detail (compare what happens when you scale down a large image with what happens when you scale up a small image).
With images boxes, it's generally a good idea to set the width or height (rather than both), because this will preserve the aspect (width to height) ratio of the image. If you set both the width and height, and they are not in the same ratio as the original image ratio, the image will be distorted. If you set just one (usually width rather than height) the image will be scaled by the same amount in both directions.
One other point to remember is that image pixels (the dots that make up an image) are not the same as CSS pixels. A CSS pixel ("px" in CSS and Xway) is defined as 1/90th of an inch, so a 300x300-pixel box will appear to be more or less the same size on a high-resolution or low-resolution screen.