Best to check with your aviation authority about what each liscence means.  Here in Canada, with a private you can fly any single engine aircraft pretty much anywhere by VFR.  Night flying and multiengine requires other rating.  This is the general all-around liscence.  You need this for other ratings, or if you want to go commercial etc.

With student... well, you know your learning with the permit.  And well, your most likely operating a training aircraft, definately not allowed to carry anyone except your flight instructor....  Pretty self explanatory.

Theres also recreational permits that allow you to fly single engine aircraft, and you cant carry more than one passenger kind of thing here.

If you want to make flying a living, commercial and airline transport pilot are pretty much like that.  Commercial i believe you can operate aircraft less than 12,566 lbs (in america its 12,500lbs).  But don't quote me on that one.  Airline transport pilot is the next level up and i think its pretty self explanatory

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No you don't.

Multi and IFR are unrelated.

The general idea is that a multi pilot should have a good pile of hours on his logbook cause twins have a tendency to be unforgiving of mistakes ... so generally pilots that go for multi already have the IFR ticket.

But that's not necessary nor a requirement that I know of ... if you are a good pilot you can just get a multi rating and fly VFR all the time. Nothing wrong with that 

Edit: I am talking about the USA here ... I don't know how it work in other countries. It might be different.

Actually (in the US), the twin rating requires only 8 hours in the plane prior to the checkride-most people get more of course.