a) Full size means size of original, if the original is narrower than the maximum the theme allows. If it's wider, then full size means scaled down to that maximum. Naturally, the maximum is usually the width of the main column. In the theme you're using it's 640px. When you upload an image that's wider than this, and you select the full size option, the theme will automatically insert a 640px wide version of the image.
b) The Thumbnail, Medium and Large options are supposed to be three different options for further scaling down. You set the defaults for these options (in Settings > Media): you set the width for thumbnails to whatever you prefer, and you set the width for the medium and large options to, say, around 1/2 and 3/4 of the main column width.
c) I checked a few of the images you have uploaded and inserted. The originals are 240dpi, and wider than 3000px. There's no point doing that when browsers display images at 72pi and when the maximum in the theme you're using is 640px. Even if you want the inserted versions to open a larger view when clicked (is that intentional or not?), no normal user has a 3000px wide screen. Uploading such huge files means you waste your storage space and you increase the loading time of your pages. Plus you get worse quality on the post, because images downsized by WP lose some color and sharpness - see here:
So the ideal way is to use an image editing application or an online tool to downsize copies of your images to the desired pixel width (640px or less), and upload and insert those copies (in full size).
As for the spacing issue, we can't really say if we can't see the post. For starters, did you copypaste the content from another source such as Word? Do you mean space between paragraphs? If so, try this: highlight all in the Visual editor, select Paragraph from the Format tool (row 2 tool 1), switch the editor to Text and back to Visual, click Update.