In what kind of orbitals do the lone-pair electrons on the singly bonded oxygen of methyl acetate reside, and are they in the same plane as the group

Both lone pairs reside in sp3 orbitals; they are co-planar with the CH3 group.

Explanation:

In the compound, methyl acetate, the  lone-pair of electrons on the singly bonded oxygen atom is accommodated in sp3 hybridized orbitals.

If we look at the compound, we will notice the both lone pair of electrons on oxygen are accommodated in sp3 orbitals which are co-planar with the  CH3 group  in the molecule.

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