Are the seeds in a single capsicum fruit genetically identical?
No, the seeds are not genetically identical.  Each seed come from the fertilization of an ovum with a sperm from a separate pollen grain.  Since each pollen grain can come from a different plant, the seeds will generally differ from one another.
Additionally, even ova from a single plant will not usually be genetically identical to one another.  This is because the process that creates the ova (meiosis) shuffles the genes of the parent plant on then places only half into the ovum.  The same kind of shuffling goes on in the creation of pollen grains.
In the chili pepper genus (Capsicum), plants are predominantly self-pollinating. This means the majority of the pollen for the seeds in a fruit will come from the very same plant.  This generally reduces the amount of variation seen in the offspring compared to complete cross-plant pollination. Some cross-pollination can nevertheless occur if there are other varieties in the neighborhood.  The fruit will not show the effects of the new genetic combinations present in its seed, but only a plant grown from the seed will make the differences evident.