If two Muggle parents conceived twins, can one of the twins be magical?

Question

If two Muggles conceived twins, can one of the twins be magical? Same goes for when two magical parents conceived twins, can one of the twins be a Squib?

Answer 1

J.K. Rowling describes something pretty close to what you're looking for on Pottermore. The founder of Ilvermorny (the american Hogwarts) and her muggle husband had twins, one of which was a squib, the other a witch.

[...] the twin girls to whom Isolt had now given birth: Martha, named for James’s late mother, and Rionach, named for Isolt’s. [...] Martha, the elder of James and Isolt’s twins, was a Squib.

From this, we can assume the same kind of thing can happen in a muggle or an all-wizard family.

Answer 2

Yes.

We know from J. K. Rowling that

Muggle-borns will have a witch or wizard somewhere on their family tree, in some cases many, many generations back. The gene resurfaces in some unexpected places.

There are three ways for twins to exist, and at least two of them could result in twins of differing magical ability.

Fraternal twins

Fraternal twins happen when two egg cells (instead of one) are released and each fertilized separately. They're no more genetically similar than "regular" siblings, so one could be magical and one not (either a Muggle-born and a Muggle, or a non-Muggle-born and a squib).

Identical twins

Identical twins happen when one egg cell is fertilized, creating a new person, but then that person divides into two before continuing to grow. Identical twins are genetically identical, except for small, random in-utero mutations. They could only be a magic/non-magic pair if it were possible for one twin to mutate in or out of being magic, so it depends on more precise knowledge about the genetics of magic than we know. If Muggle-borns are all magic by heritage, not mutation, then I think we can rule out that one identical twin could develop the "magic gene" (allele) by mutation. It might, however, be possible that both twins have the "magic gene" but it's only turned on in one twin because of a mutation (either turning it on or off).

Semi-identical twins

Semi-identical twins, a more recent discovery, happen when only one egg cell is released, but divides before fertilization, with each resulting cell then being fertilized separately. These twins are half-genetically identical, so one could be magical (through his or her father) and the other not.