I can download and install apps from Google Play but I can't download any zip file, 7z file, Google Drive website file, mp3, torrent, etc on my phone. I haven't changed any settings as far as i know and I can't download anything from any trusted site. Even the bittorrent app's downloads turn red and stay at 0 despite being known good files. This happens when I try to download files on 4g and also wifi. How can I fix this without doing a factory reset?
Check for Restricted Background data. If it is enabled then you will have problems while downloading irrespective of it being 4G or Wifi. Go to Settings -> Data usage -> Download Manager --> restrict background data option (disable).
You could try any downloader like Download Accelerator Plus (works for me). All you need is to open your website in its local browser or provide download url in the app. Below is screenshot of the app Browser where you need to search in order to download. Then save it in your sdcard or internal storage when you see download option.