If you really have to, as in, you cant afford to purchase another pc, then yeah why not, just make sure you have it in a good place to keep it cool and/or get a cooling fan for laptops, i have one that works well to keep my laptop cool.
It is possible to run a web server on your laptop, but highly recommended that you do not if you are wanting to launch it as a production server.
I have in the past ran a web server on my laptop when I had been traveling without internet to keep up with development on a few websites.
If you are wanting some simple software to assist you in this, check out WAMP Server or xampp. They are great for quick setups and come with Apache, MySQL and PHP. They are only recommended for development servers though. They can be production server quality if they are configured correctly.
I think its possible but i cannot turn my laptop 24/7 for that. besides, it would be more of a hassle and you might want to have a shared plan for that.
Yes, it's very possible. All you need to do is to install all the required softwares on your PC.But Cost effectiveness - what you would pay in terms of electricity and bandwidth (if your site has a lot of traffic).