You don't have any downloadable files. You will see your processed files or in progress files from current and previous sessions here.
This page will show you all the in progress and processed files in File Cards as shown on Image 1 and 2 (below). In progress files are files that XConvert is still processing and processed files are files that are completed. Progress bar with percentage completed will be shown on File Cards for in progress files. At the footer of each card contains some useful buttons which allows you to perform actions like download file.
Image 2 - Completed file example
If you are located far away from the server that processed your file, then the network connectivity between you and the server could be really slow. There is nothing much we can do about it.
It is impossible to tell exact output size before compressing a file. Sometime depending on the configuration, XConvert might produces larger output files. You can always use Re-edit button to retry it again with different set of options.