path for documents:
NSString* _path = [NSSearchPathForDirectoriesInDomains(NSDocumentDirectory, NSUserDomainMask, YES) firstObject]
array with file names at _path
folder
NSError* _error;
NSArray* _fileNames = [[NSFileManager defaultManager] contentsOfDirectoryAtPath:_path error:&_error]
for zipping try to use ZipZap:
https://github.com/pixelglow/zipzap
40mb – is small file for this =)
solved What is best way to create zip file and save to Documents in iOS [closed]