How can the Network layer know the destination IP?

Clarifications

Header
The header features source and destination MAC address, the Ethertype protocol identifier field and optional IEEE 802.1Q VLAN tag indicating VLAN membership and traffic priority.

or maybe I mis-understood your question

When you put the url in the browser, a number of thngs happen, but basically the browser sends a query out to your local Domain Name servers and they look to see if there is an A record which is what translates the domain name to an IP address. If one isn't found then it goes to the next level which is your ISP and does the same check. This keeps going until it hits the root level servers (the brains to the internet so to speak). Once it has this IP address then it goes on to the network which owns the address and the process is somewhat reversed, but not quite. It all depends on the network on the receiving end. It may go through a firewall or proxy NAT (network address translation) which converts the outward facing IP to an internal IP address, but in essence the request is sent on to an internal server and the webserver then takes that URL and port and serves up the appropriate web page.

What Layer 3 receives from Layer 4, the transport protocol header does NOT contain anything about the IP address (or host name). So, from where does the layer 3 brings the destination IP address? By other words, is there a common or global source of information available simultaneously to the 7 layers, or the case is that every layer can only get information from the one above it?

can use the hostname or IP address interchangeably. So if you send a ping message from one PC to another, you can specify either it's IP address or the hostname

http://en.wikipedia.org/wiki/Service_discovery
http://en.wikipedia.org/wiki/Simple_Service_Discovery_Protocol
http://en.wikipedia.org/wiki/Address_Resolution_Protocol

Layer 3 Name/IP Address would most likely be from SSDP in a non-dns non-dhcp network
The computer would then use ARP to get the MAC Address of the destination computer so it could actually send the message.