A few questions.
Are the ova of identical twin women identical as well?
Assuming they are, if Twin A and Twin B were both to get pregnant on the same day, would the eggs that are being fertilized be the same? Or is it more random?
Assuming the answer to the previous two questions is yes, how closely related would the ensuing cousins be? Would they be half-siblings genetically speaking?
The ova of identical twins are formed from genetically identical oocytes, but during the process of egg formation, the oocytes split in half, taking half of the genetic material with them 23 individual chromosomes instead of 23 pairs - during this process, there is a sort of cut-and-paste operation going on, ensuring that the resultant ova have a pretty much unique assortment of genetic material.
It is explained better here and when you look at it, you can sort of see how and why Mendel’s stuff about heritability works.
Short answer - their ova are as alike as if they were all ova from one individual. So, in the sense you probably mean, yes.
Individually, no - all ova in any woman’s body contain genetic variation, that’s sort of the point. Everyone has two sets of genes, a matched pair of each chromosome (barring rare disorders such as trisomny 21/Down’s syndrome or X0/Turner’s Syndrome). With each gamete (that is, ova or sperm) the deck is reshuffled, so to speak so one ova might have gene for blond hair and one for brown, but barring random mutation, no ova will contain a gene that wasn’t already in the woman’s genetic make-up. Since identical twins are genetically identical, there would be no way to know if a given ova came from one twin or the other. In that sense - no difference in result, no way to know originating individual - they are the same.
More random. Identical twins may be genetically identical, but they are still individuals - they have their own, distinct fingerprints, retina prints, opinions, and so forth. There is no reason to presume they would be fertile on the same days of any given month - for various reasons their menstrual cycles could fall in and out of synch with each other, just like any two other women. Likewise, the individual genetic package delivered in each of their ova would be slightly different just as any two eggs taken from a particular woman will be different.
All the offspring of identical twins (or triplets, for that matter - which does happen occassionally) are genetically half-siblings even if socially they’re counsins. With one exception: if two sets of identical twins married - boy I-twins to girl I-twins - then their children are genetically full siblings and socially counsins.
If the preceding posts were insufficiently clear, ova from the same woman cannot be expected to be identical, so neither can ova from her identical twin. However, her ova are as alike to each other as they are to her twin’s ova.