1. OpenOffice does have an equation editor. I've never used it myself, but I opened it up to try it out and found the interface a little bland, although it seems to be pretty capable. If OO doesn't suit your needs you may be able to run MS Office on Ubuntu using WINE (which is kind of like a Windows emulator).
2. OO Writer actually includes a macro (or hotkey?) that creates a numbered equation for you: type fn at the start of a paragraph and then press F3. (I found this on a website)
3. OO Calc can do curve fitting, although for some odd reason it only seems to offer linear, logarithmic, exponential, and power law fits, not polynomials. Perhaps polynomial fits are available as an addon or something. To be honest, there are probably hundreds of tools available on Ubuntu that can handle curve fitting and data analysis better than OO Calc or Excel.
4. You're not expecting to suddenly be able to get Matlab or Mathematica for free just because you start using Linux, are you?! Both programs have versions that run on Ubuntu, but you will have to pay for them, same as the Windows versions. If your workplace or school has some sort of volume license deal that allowed you to get the Windows version of either program for free, that should apply as well to the Linux version. There are also several free programs that aim to provide roughly the same functionality as Matlab and Mathematica, although from what I've seen none of them are quite as good as the original. They may well be fine for your purposes.
By the way, if you're going to switch to Ubuntu I would strongly consider you to give LaTeX a try as a replacement for MS Word. In fact, even if you stay on Windows, take a look at MikTeX (the Windows version). It definitely takes some getting used to but it makes typing up technical documents, especially equations, so much easier.