connect a computer to a website using HTTP Protocol. Is this possible ?
Of course.. that's exactly what happens when you a browser application to connect to a web server. So, if you wanted to do this outside of a browser/web server system, you still need to have at least two components... A client application that uses HTTP to communicate and a computer running a listener on port 80 and is programmed to accept HTTP packets.
static IP Address
A static IP address is really not related to HTTP. The host and server could be configured with static or dynamic IP addressing. The only difference is that the static is applied and the computer will not try to negotiate an IP from a DHCP server. To get a static IP, you need to work with your system/network administrator so that a static IP is given to you from the pool of available IPs on your network.
To do what exactly? Your description is too generic. What do you need or function is needed that your browser is not providing? The browser is the perfect example for what you described. It connects to a web server and requests data using the HTTP protocol.
connected to a computer that having a valid Static IP Address
First, you have to make sure that the static IP address you have been given has been NAT'd between your GSM Modem and the Internet. From that device, you can go to a site like My Source IP
Assuming that this static IP is directly accessible, your provider would have to allow inbound traffic on port 80.
Next, you need to have some type of application listening on port 80 on that host. What will this application be serving on port 80? HTML? If so, you would load a web server. Will you be transmitting some other type of data via HTTP? This is out of my area of expertise, but you ask is it possible, and my response would be yes, anything is possible given enough time and resources. This requires additional research.
Finally, depending on what content you will be serving, the client making the request for data, using HTTP to this target computer on the GSM modem, this needs to be determined as well. Again, sorry...beyond my area of expertise.
Since you mention PHP, I am assuming this is HTML that you are sending back to the user agent??
have to listen the COM1 port.
I am not sure what you mean by that... I am assuming that the modem is on COM1? I dont see that as an issue because what ever service you will be running that will be listening, say a web server, does not need to be aware that there is a modem on COM1, because I assume that this modem connection is creating some type of virtual adapter that your application (say the web server) can bind to? The web server simply needs to be able to see an IP available for use. The lower layer services in the OS take care of how the computer is connected to a network. The applications are not concerned with if the computer is connected to a wired NIC, wireless network, etc...