Time capsule block many app on iphone

I suspect you have a double NAT.

Please give us full details of the network.

What broadband do you have?? If this is a building ethernet connection that is a problem. You are forced to double NAT in order to use multiple devices or even just wireless.

I'm using Airport Time Capsule in my home networking.

But I can't load pictures on Facebook app, Appstore I can't see anything, I can't load anything in Music app and Itunes Store.

I change for another device, TP-Link and can't load anything in these app mention above.

When you change to the TP-Link and it also doesn't work. then the issue is not the TC.. it is the network supplier.

TC might have issues with port mapping for an App that is not setup correctly.

List the apps that don't work and try and manually set port mapping for them.

Also I would make sure your client device is getting DNS correctly.. using google DNS in the TC is not standard.. and might have issues. Usually it is better to set it to fully auto.. and allow the clients to be set manually.

I will try set port for each app tonight?

Where can I find the port that the app use?

You need to google for each one.

The app has to give a list of ports required.. it should be in the details of each app.

Most probably just use standard ports like 80 or 443.

It is the special ports.. and if they are already used that causes problems.

Leave it blank.. when the Airport connects it will get the DNS via dhcp from the ISP.