Here's my take your questions. Your mileage may vary.
1) For tools, everything except R + LyX is icing on the cake. In my case, I use Emacs + ESS + AUCTeX, Org-Mode, the terminal, and RStudio. Again, R + LyX will get you by in a pinch.
2) LyX gets rid of (read: hides) a lot of the extra folders/crap of which you need to keep track. I just opened one of my projects and I just had a root directory and an /img folder, for holding those images that aren't generated by Sweave. Everything else is, well, icing on the cake.
3) With LyX, you just get up and go! The point is you don't have to fiddle with things like documentclass or anything else. Just start writing, and you can polish everything else later. Yes, sometimes I will run a lengthy computation and save it in an .RData, which I load later. I don't fiddle with the R code (i.e. .r file), because I can tangle that later. (At least, you used to be able to).
4) If it's a very small project, I use RStudio. If it's a medium-sized project, I open LyX and get started. If it's a huge project with lots of coding, I'll usually use Emacs/ESS and copy-paste to LyX later. If it's a REALLY huge project, I've used LyX but more recently Emacs Org Mode.
5) I use the same R packages that I use everywhere else, and LyX is not a term in that equation.
6) Yihui Xie has a lot of great stuff.
Some general comments to help your decision to keep/abandon LyX:
a) LyX has a knowledgeable community to help you, and they are responsive.
b) I've worked on projects large and small with LyX. It's really powerful for 1) something quick or 2) something huge, where you need to label, do an index, and/or bibliographies. This functionality exists for Emacs but with LyX it's out-of-the-box, follow-your-nose.
c) LyX isn't so good for instant-preview of your LaTeX and/or Sweave code (which can be a real PITA for Sweave figures). I've found that Emacs Org-Mode does both, while AUCTeX does the former.
d) and BTW: now that I think about it, I HAVE used text editors (Emacs/ESS or RStudio) to run/polish code before pasting in the .lyx file, simply because when your project is big it is unproductive to compile the whole thing just for a few lines. When the project is small, it doesn't matter either way.
e) and BBTW, @Tormod is right that collaboration is an issue, but it always is and will continue to be for the foreseeable future. With LyX you can export to Sweave/LaTeX/HTML/OpenDocument, and if none of your buddies use anything on that list then you need to find different buddies. :-)
f) B^{3}TW: the siren song which initially lured me to LyX was its automatic handling of figures and tables - they couldn't be simpler. You can mix and match whatever figure filetypes you like, and LyX knows which packages to load and conversions to do such that it just works. This is a pain that I am enduring again as I do other projects with Org Mode, AUCTeX, and RStudio.