Not sure of the downloading issue, but heres a few AnySIM 1.3 tips I can think of:
BSD subsystem used to be required, not sure if still is, but grab it anyway.
Turn on Airplane mode before you run it. Afterwards, you will still be in airplane mode probably, but the icon will have been replaced by "no bars", so just go back to settings and turn airplane mode off, hopefully you see your carrier then.
Set autolock to Never
If you keep getting told to set autolock to never, when you have already, it is due to the app looking in /var/root rather than /var/mobile to check this setting. You can use mobileterminal or ssh to copy your /var/mobile/Library/Preferences/com.apple.springboard.plist to the corresponding location on /var/root. You may need to adjust the permissions on the file too, so anysim can read it correctly.
It goes without saying, but don't get "bored" with unlocking and quit the app midway, as this will leave you with a corrupt baseband at least. With ziphone now, its not too much of a hassle to restore this, but still, don't do it!
Thats all I can think of, hope it helps someone.