Hi!
I am working on my master diploma and I am designing a mixed signal 
ASIC.
So from my (very limited) experience:
-) For normal RTL designs you trust in the synthesis and PnR tools. You 
are still working with the standard cells you have to know if something 
is faulty.
-) Sometimes you want to design something that is not synthesizable or 
you want to do some analog simulation because you want to know the exact 
timing.

For the degree of documentation: we got everything from the factory 
regarding the std cells. By that I mean the layout (together with the 
techfiles I can do post layout simulation) and the digital libaries used 
for synthesis and STA. I don't know what else is needed (you could make 
the digital libs yourself if you have way to much time). So the hardware 
is fully documented. I don't know if this is normal or if other fabs 
only give away abstract views of their cells.

But in most uses you should trust in your synthesis and PnR tools. Doing 
timing analysis by hand is nearly impossible (especially when you start 
talking about setup and hold violation with different corners). I think 
creating an 8 bit counter would take some days :D

Examples:

1) testbench code (models of pads, analog, drivers, etc.)

2) when interfacing hard-macros and you need hazard-free logic (e.g. 
real multiplexers instead of AND/OR logic)

In our ASIC designs at work, the only thing we write at gate level is 
our clocking infrastructure, since glitch-free operation is vital here 
(and since you need to use balanced-output clock gates rather than 
standard logic cells)

For everything else, synthesis will do a better job than you of 
fine-grained optimisation. However, you can help synthesis out a lot by 
specifying a more efficient structure at the high level, and this 
requires you to think about what you expect your synthesis output to 
look like.