Yes, I would guess that tgiokdi is right.
I just made a short test and if the "medium" and "large" size defined in wp-admin => settings => media are larger than the original size of the picture uploded, these format are not generated by wordpress...
By default, the large size in WordPress is 1024 x 1024 and the full size of your picture (the original size of the file itself), in the screen capture I see, is 536x290... This is why you don't have the "large" option...
---
Now, why the link doesn't appear automatically in the ? ... Well, I don't know... On my side, if I choose an image in de media library or uplod a file from my computer the "file url" is always there by default...
Hum...
S.