Is it possible to download a very large file at my connection speed without any interruptions and incomplete download problems?

Yes, it is possible even if it is a little difficult and time consuming.  You require an FTP program that resumes broken downloads.  Cute FTP is one such shareware program available at http://www.tucows.com .  You can use this to download a large file over many days because you can resume the download from where you left it each time you connect to the Internet.  Please remember to obtain the FTP server name and username and password for the site from which you want to download your program.