No there are various techniques using the appropriate software. VirtualDJ is a great program to do mixing only using the software within your computer. Connect your laptop to a good set of speakers and it can be an acceptable replacement.
You do not need to have a separate mixing console if you just want to basically mix songs together for parties. You can get software on your computer which will do that. You won't be able to do any scratching of the songs or cool effects that you would get with a mixing console or turntable.
Depends on the program. I recommend using Native Instrument's Traktor program. It has anything an aspiring computer DJ could ever need and you definitely won't need an external mixer if you have this program.
No, you don't absolutely need a separate mixing console. There are a lot of programs available (both free and for a price) that allow you to play and mix music right from your laptop screen. But if you like, you can use an external mixer as well.
Isn't necessary because there's a lot of programs that can replace the table console as virtual dj, dss dj, zulu dj, dj jukebox, e-mix, ots turntables and more.
I'm pretty sure you DONT need to separate sound mixing console if you have a laptop and a turntables, because all you need to do is to buy CDJ and connect it to your laptop