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HI MinHP, The test with turning off wifi and connecting the network cable is to see if the PI can still get internet access through the network cable, the iphone won't be able to connect at this point as the wifi is off.

If you think you have a weak signal try using a different wifi channel as other routers in your area may be causing the issue.
in /etc/hostapd.conf change channel=8 to different channels and try again.

I have a 5Ghz setup but I haven't used it much, there also seems to be more limitations in some countries and less reliable in densely populated areas than 2.5ghz N.
I haven't spent much time on my pI'S latley but I will add it as an option when I get time.

Are you able to connect to the hotspot from your laptop and get internet access?
If so then the issue will be with the Iphone.