1.if a stationary loop is removed from a time-varying magnetic field region, will there be any electric field associated with it?

2.will there be an induced e.m.f. across a rod if it is placed in a time-varying magnetic field region?if so, why?

3.i have heard that in some instances, it is seen that a magnetic force is found to do work.can you please provide some examples(in the form of problems)?

no as far as there is no electricity in the  conductor.........

yes there wud be an induced emf generted coz a tyym-varying magnetic field produces magnetic flux that generates emf in the rod.....

in class 12 physics ncert txtbooks, u wud surely find problems associated with it... for eg, if a magnet is kept stationary and anothe r magnet with the same polarity is brought near it,the stationary magnet produces a magnetis force that is, of replsion, which pushes the second magnet outward....this shows that magnetic force can do work, here moving a magnet...{same is the case for attraction of magnetis objects by a magnet...}

Hope u found this useful.........