If you select only one image size, then Juicebox-Pro will have no option but to display this image size in the gallery.
However, if you select multiple image sizes, then Juicebox-Pro will display the most appropriate image size for the device and screen being used to view the gallery (according to the logic noted in the Multi-Size Image guide).

In order to generate 'Large' and/or 'Small' images (and to resize the source images for the 'Medium' images, too), the 'Resize Images' checkbox must be selected.
If the 'Resize Images' checkbox is deselected, then the source images will not be resized at all (no matter what image sizes have been selected in the 'Set Images Sizes' control panel) and the source images will simply be copied across to the gallery's 'images' folder for use as the imageURL ('Medium') images.

No matter what image size is displayed, the images in the gallery will be scaled depending on the value of the imageScaleMode configuration option (SCALE_DOWN, SCALE, FILL, STRETCH, NONE). Short descriptions for each of those values can be found in the Main Image section of the Config Options page.

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If you select the 'Large Images' checkbox, then an additional 'large' set of images will be generated for the gallery and Juicebox-Pro will use them under the following conditions:
(1) The 'large' images will be used for the main gallery display in Large Screen Mode when a retina screen is being used to view the gallery.
(2) The 'large' images will also be used when an image is opened in a new window (via the 'Open Image' button) in both Small and Large Screen Modes and when the gallery has been expanded (via useFullscreenExpand="TRUE") in Large Screen Mode.
The concept behind having a number of different image sizes is to serve images appropriate to the viewing device (and to prevent large images from being served when small images will suffice).

No. In Small Screen Mode (which your gallery uses), the 'small' images are used after clicking a thumbnail unless there are no 'small' images available, in which case, the 'medium' images (which are available in all galleries) are used.

You can always increase the resolution of your images and bump up the quality (from the default value of 80) but the larger your images, the longer they will take to load.
The default values (of 1024px x 768px at a quality of 80% for 'medium' images) are usually a good compromise, resulting in images with a filesize of approximately 120KB, but if you feel that your images would benefit from having a larger resolution (or a higher quality) then I would recommend that you try larger values in the 'Set Image Sizes' control panel.

That is fine but please bear in mind that when using SCALE, Juicebox-Pro will dynamically scale up small images to fit within the gallery's image area if they are not large enough (as well as scaling down large images if necessary). This may reduce their visual quality. SCALE_DOWN (the default value), on the other hand, will only scale down large images (and will not scale up small images).

Your gallery forces Small Screen Mode (designed for small screen mobile devices) to be used on all devices and in al browsers (by setting screenMode="SMALL"). In Small Screen Mode, if 'small' images are available, they will be used in the main gallery display (after selecting a thumbnail).

A Multi-Size Image gallery works best when screenMode="AUTO" and Juicebox can choose between screen modes (which has a bearing on which image size is used).

There is no real problem with setting screenMode="SMALL" but, knowing that Juicebox will use 'small' images for the main gallery display (if the 'Small Images' checkbox has been selected), just make sure that your 'small' images are quite large. There is nothing stopping you from changing the resolution and quality of the 'small' images to whatever you like (within the working parameters of JuiceboxBuilder).

Also, knowing that your Juicebox gallery will always be displayed in Small Screen Mode and that Juicebox will not be using the multiple image sizes as diversely as it would if screenMode="AUTO", you might like to just have one set of images for your gallery (the 'medium' images) and not worry about generating 'small' and 'large' images'. Just make sure that your 'medium' images (which will be used for everything except the thumbnails) have a good balance between resolution/quality and filesize.

If you are not resizing images in JuiceboxBuilder-Pro (the 'Resize Images' checkbox is deselected), then all values in the 'Set Image Sizes' control panel are ignored. JuiceboxBuilder-Pro simply copies your source images into the gallery's 'images' folder.