For the uplight, you could go a few routes, especially with respect to dimming functionality. And some fixtures don't support dimming, so you need to figure that out. To that end, I suggest you think through the use cases. For example, the use case that I think I'd appreciate most is late evening, after you've retired to another room of the house, at which time a mellow indirect glow from the skylight cutout would be particularly pleasant. You might also want the more light from this source on occasion, in which case you'd want brighter lights on a dimmer. That being said, here's some options. I'm thinking two, centered on the skylights, mounted near the bottom rim of the cutout (just above the beam probably). Regarding the pendant, I know that selecting pendants is hard enough without more to think about, but one downside of a single pendant vs multiple pendants is thhat single sources create worse shadows. And the clear glass pendants above exacerbate this harsh shadow problem by being point sources, whereas the Fillsta, for example, mitigates this problem because it's effectively a uniform 31" sphere of light. This large diffuser also makes it possible to use a brighter source. For example, you could put a 300W equivalent CFL in the Fillsta, but such a bright light would be unacceptably harsh in a point source like the clear glass pendants above.

It is a large kitchen and completely open to the family room. The center island is 128" (we refer to it as the cooking island). There are also perimeter cabinets and a 48" gas range. The hardwood floors are being installed now and the cabinets will be installed in about a week, so I don't have a good picture yet to capture the size of the space. We have 10 foot ceilings and an entire wall of windows, so everything is very open. I have attached a picture from a few weeks ago. It is from the perspective of the kitchen looking into the family room. The "island" you see is just the support for what will be the raised portion of the island (the bar top). I hope this helps.

Generally, a pendant light over a peninsula or island should be spaced about 24 inches apart. You don't mention the length of the counter, but 7 lights seems a little (lot?) excessive. Maybe 5 lights at the most?

IMO forget any light fixture in a kitchen that uses Edison bulbs. All lighting in a kitchen should provide good lighting so look for something in an LED fixture with 4000K bulbs I have no idea of the size of the island but usually 3 pendants ate the norm and If all you want is a linear one it will need to have either the electrical at one end or you need a new electrical box in the center of the 2 old ones. Maybe look at a track type light where the electrical can be anywhere and then choose the pendants you like to hang from it at the proper spacing