1. How to know, whether the modem is enabled for wi-fi or not.
By going into modem setting page from 192.168.1.1
2. I have read in many sites that the configuration of the modem can be done by going to site 192.168.1.1. But when i try to go to that site through IE, it is not opening.
If 192.168.1.1 isn't working then maybe your modem/
router address is different.
Run cmd.exe in Administrator Mode and type ipconfig, note what the Default Gateway address is, this is your modem/router address that will give you access to various settings.
3. Also i want to connect to this modem through my
Samsung Galaxy S Duos smart phone. While enabling the wi-fi in the phone, it detects the modem and tries to connect it and gives the message "Obtaining IP address", but it remains in that status for sometime and after that it does not connect. So how to connect my phone to the modem.
This could happen because of various reasons, If you connect to the Internet through a dialer or only through the PC's operating system then the modem isn't in an always on state(Wifi device like a Phone won't know or can't connect to the wifi if modem is setup to connect to the Internet only through OS, it needs to be in an always on state meaning,
this gives the steps) or
this
4. Is it required to connect to broadband in my PC to get accesss in my phone or just making on the PC & Modem(Without connecting it to Broadband) will suffice for connecting with the phone.
Already answered. It depends on how the modem is configured, if username and password are provided in modem/router page settings then both the PC and the Wifi device will connect automatically, but if username-password are configured only on PC OS then a wifi device can't connect even though i knows a wifi access point exists.
5. How to password protect my modem, so that it can not be used by anybody.
Every different model of router/modem has a different setup in its settings page layout, so just browse through it and look for password protecting access to your router(this is to prevent your modem settings from being changed by someone else).
You can password protect the Wifi Access Point that you create with your desired level of security from the settings. If you don't use any security and make it an open Wifi then anyone can connect to it.
Another way is to block access by
Mac Address blocking. Note down your phone/wifi device's Mac Address and give access to it only, this way even if you make an Open Wifi no one else will be able to connect to it since every wifi device has its own unique Mac Address.
This solution is sometimes forced on users, as often setting a security setting on the Wifi Access point like WPA, etc doesn't work, its the fault of the modem/router and the above solution of Open Wifi with Mac Blocking is a workaround for that(personal experience of having a weired modem).
Note that these measures can be hacked through but only by someone who knows what he/she is doing, its reasonably safe for everyday users.
Hope this helps.
Also you might want to enter the Default Gateway address in the Internet Protocol Version 4 (TCP/IPv4) Properties as is explained in the link provided by the user above me.
Subnet
mask would be same and the IP address could be as page mentions.