How can I access files on my network from my iPhone?
I recommend FileExplorer Free.  I just installed it to access files that I wrote on a SD card in my WiFi router.  I have an iPhone and iPad.  FileExplorer can use CIFS, SMB, FTP and others.  It can read many formats such as PDF, video, photos, music and Microsoft Office.
There is  priced version for five dollars.