For preserving the filetime after uploading the files, your FTP server does not support one of "MFMT", "MDTM", and "SITE UTIME" command. But BestSync can still synchronize files correctly without these commands.
Please ignore the file size when synchronize the Outlook, because the file size in Outlook side is the size of the message, in otherhand, the file size in file system is the file of the .msg file. They are different.
Please synchronize the Outlook of two PCs once to see if the messages that need to be synchronized will be decreased.