I think you have to assume that any object in 'blocking' contact (i.e. it is in contact with a body in the direction it's trying to move), the impulse across the contact must be equal to the component of the collision impulse in that direction (i.e. the first object can't move in the direction of the contact). I don't know if that works when you're in contact with more than one object at once though as unless the contacts are orthogonal the impulses will affect each other. I'd need to do some more thinking about that.

Impulsive collisions are instantaneous. If you detect multiple collisions during your timestep, the only situations in which they're genuinely simultaneous are artifical ones (i.e. your objects initially started perfectly axis aligned etc). If you handle the collisions during the timestep in any arbitrary order and continue processing until there are no more collisions, then you will achieve a realistic result, even though the actual result might depend on some internal details like the processing order.

The standard collision law that you've already implemented is only valid for pairs of objects at a time (though I think there are other "laws" that more bodies in simultaneous contact). Trying to handle all collisions at once with this law (LCP approach) won't work.

There was a discussion some time ago here. Anonymous Poster should be viewed as a "devil's advocate" when reading this (I think!).