Re: corner analysis of Vth
do not disregard the sf/fs cases, as they will tell you which variety of transistor is causing the most variation in your circuit performance, but yes, skew cases (of that extreme) are uncommon in production.
yes, you should expect some skew between your NMOS and PMOS as the body of each is a different well, but usually the variance in skew is small compared to the overall fast/slow trend.
think of the n-well process. substrate doping varies quite a bit. n-well doping varies less, but still is significant. s/d implants are usually better controlled, threshold adjust is about the same as s/d implant, and gate oxide thickness varies depending on fab - some are very good, some have lots of variation.
substrate doping affects both NMOS & PMOS in a trend, where as n-well only affects PMOS - one source of skew. s/d implant may cause rds skew but not Vt, threshold adjust affects both at the same time, and finally tox skews both at the same time.
now you can see it would be odd to have high threshold on one device and low threshold on the other - most CMOS processes are pretty resistant to that.