High-spin neutron star Suppose a large neutron star were to be spun-up by a particular pattern of mass-accretion. The increased centrifugal force could presumably mitigate the increased gravity thus delaying gravitational collapse. How far could this process be taken?
 A: Here is a link to a paper where rotationally delayed collapse is seriously considered:
http://arxiv.org/abs/0804.0594
It is found likely to occur in some cases, but the delays are of order 10 milliseconds,
(which is significant for gravitational wave detection.)
A: The maximum rotation rate of a neutron star is: $\Omega=(M/R^3)^{1/2}$ where M is the non-rotating mass and R the Radius. I admit that I havent worked this out, but I found it in a thesis I have been studying in connection with another Stack question "Geometrical and Physical Aspects of Rotating Neutron Star Models". Around equation (4.5), there is further discussion of conditions and variants.
http://www.icg.port.ac.uk/theses/white.pdf
Note that White Dwarfs are similar objects which are held together by electron degeneracy pressure - and may obey similar equations.
A: Excerpt from a report I once wrote on this topic:
http://bytepawn.com/pdf/Exciting.pdf
Gravitationally bound compact objects --- such as neutron stars --- cannot have pulsar periods less than 0.3msec. The pulsar period is of course radius and mass dependent, but
is bound from below by a neutron star just on the verge of forming a black hole
singularity.
Strange quark stars are hypothetical objects qualitatively diﬀerent from other
compact stars such as neutron stars. First, they are composed of strange quark
matter, a hypothetical form of matter consisting of equal part u, d and s quarks.
This phase must be of lower energy than hadronic matter for a strange star to be
stable to quark fusion. Second, unlike neutrons stars which are held together by
gravity, strange stars are bound by the strong interaction. As strange stars are not bound by gravity, they are free to occupy the sub-millisecond pulsar region.
EDIT:
The limiting angular velocity for a gravitationally bound star goes as
$(M/R^3)^{1/2}$.
This comes from Newtonian arguments (centrifugal vs. gravitation force). The GR version turns out to have the same form, just a different multiplicative constant ("accurate to better than 10%" according to Glendenning). So, to maximise the angular velocity, you maximise M and minimize R. But, if you do that, you make the start more compact, and eventually it forms a black hole! Quantitatively, there's your limit.
But note that the limit is not one number it's actually a function mass M. To get rid of R, use the fact that according to Einstein's equations of stellar structure (Oppenheimer-Volkoff equations for hydrostatic equilibrium)
$M/R < 4/9$.
In the end the formula for the rotational period is:
$P > 0.167 M / M_{sun} [msec]$
For more please check the book Compact Stars by N. K. Glendenning, it's very good.
A: The problem with this idea is that you get a fairly modest reduction of the pressure at the center of the star because the poles of rotation don't feel the effect. The detailed calculation would have to be relativistic and assume an equation of state for neutronium. 
Last I heard theory and observation could put only fairly broad limits on the real equation of state.
A: Neutron stars are stable end points of stellar evolution.  So long as their mass is less than whatever the modern, updated version of the Chandrasekhar mass is (something like 1.5-2.2 times the mass of the sun), they won't collapse to a black hole.  
If they're over the Chandrasekhar mass, then the core will  be the most compact part of the NS, and centrifugal forces will be less important, because the mass will be close to the center of rotation, and the core will collapse first, and you'll get a NS supernova.  
I don't get the premise of this question.  
