The so-called Modified File there is actually the Preview. That was used for sharing images with other applications. It was a medium quality version of the shot, frequently missing metadata, or at least unreliable in its treatment of metadata. The idea is that this would be shared to email or a word processing document as a "good enough" version of the photograph and save you the bother of exporting every single time you wanted to send a pic somewhere.
Exporting is there to give you more control over the filetypes and quality of your exports.
You have to distinguish between file metadata and photo metadata. They are quite separate things. The file data you refer to is accurate to the extent that it reflects the date these individual files were created. However that has nothing to do with the date the photo was taken, which is preserved in the photo's Exif metadata.
The variation in file size is down to the quality of the jpeg, that is, the amount of compression applied when creating it. Higher quality means larger file sizes. This is why it is quite possible to get exports of a photograph that have a larger file size than the original. Essentially, the app is applying less compression than the camera did, that's all.
Photos is not the same as iPhoto. There is no "modified" version that can be exported. But you can export better quality - or lower quality - options in the File -> Export dialogue. Drag and drop from the Photos window will yield the Preview.