AppStore looks too slow. Is there any way to download El Capitan without AppStore?
The short answer is no - Apple does not provide any alternative method. A short analysis is something is massively wrong with your network or your computer since 10 hours to download 6 GB of data is something that would bring Apple's iTunes / App Store / software update service to a crashing halt if it affected everyone.

Now - the answer is also yes. Once you or someone you know has downloaded the Application to install El Capitan, you can install it to USB stick and share it, but this is also how many malware get distributed when people find some random site on the internet and download El Capitan from a site and don't verify checksum.

Apple does allow people to operate a caching server so that when the first person on a network segment downloads a specific app or book , it gets cached locally. If you can VPN to a better network - or one with caching server, you might get a far better download speed to your Mac.

Look in /var/log/commerce.log for an entry like:

May 29 07:54:07 mac storedownloadd[37414]: ProgressObserver: Created a placeholder at /Applications/OS X El Capitan.appdownload to represent download progress
May 29 07:54:08 mac storedownloadd[37414]: sending status (OS X El Capitan): 0.000000% (-1.000000)
May 29 07:54:09 mac storedownloadd[37414]: sending status (OS X El Capitan): 0.002089% (-1.000000)
May 29 07:54:11 mac storedownloadd[37414]: sending status (OS X El Capitan): 0.004216% (1505.469385)
May 29 07:54:13 mac storedownloadd[37414]: sending status (OS X El Capitan): 0.006556% (1382.851770)
May 29 07:54:14 mac storedownloadd[37414]: sending status (OS X El Capitan): 0.009006% (1307.710558)


After a while, if you have good network (this is a MacBook using AirPort WiFi in the US):

May 29 08:00:17 mac storedownloadd[37414]: sending status (OS X El Capitan): 0.548568% (814.645701)
May 29 08:00:18 mac storedownloadd[37414]: sending status (OS X El Capitan): 0.550823% (812.247625)
May 29 08:00:20 mac storedownloadd[37414]: sending status (OS X El Capitan): 0.553163% (809.416475)


At nearly the end, an installClient process runs to finish the installation and the time estimates usually are conservative in that you finish before they predict at that point.

May 29 08:03:19 mac storedownloadd[37414]: installClientDidFinish
May 29 08:03:19 mac storedownloadd[37414]: sending status (OS X El Capitan): 0.967742% (3.000000)
May 29 08:03:19 mac storeassetd[37257]: SoftwareMap: No app was found with bundle ID com.apple.InstallAssistant.ElCapitan to upgrade to 1.7.46
May 29 08:03:19 mac storedownloadd[37414]: sending status (OS X El Capitan): 0.967742% (3.000000)
May 29 08:03:20 mac storedownloadd[37414]: sending status (OS X El Capitan): 1.000000% (0.000000)


So, for this computer it was 9m 13s to download and install. I suspect the download was already cached on my OS X server.app running on a Mac Mini - so you might watch your log with a terminal command tail -F /var/log/commerce.log and maybe try a different network or see if a friend you trust has already downloaded the file?

Lastly, be sure you are looking at the correct file. Others have mistaken the name or requirements and had not the issue you report. From your details, you really have a bad service on this one file and not something you could fix yourself.