Technically yes. You'd need to figure out the project cost though

You need to know the brand and model of your recessed housings to be able to browse a catalog and choose the trims and lamps that can improve the lamp concealment. New homes like your new one are often being built with inexpensive IC rated housings & trims. These have a stop on the socket assembly which keeps the lamp from being raised up higher in an attempt to control heat since the housings can be covered in insulation. Your 12 year old CA home probably had non IC rated housings which lacked the stop. There are more expensive housings and trims which fix this and there are some airtight trims which also can improve on this hopefully with the housings you have. If you want more detailed info then you'll need to provide more information.

I agree with Mike. Almost every recessed light I've ever used (be it old work or new) has a junction box attached and you can certainly daisy chain from one to the next (perhaps even add an additional connection). Putting it behind sheet rock provided you can get to it by pulling the fixture (without destroying the sheetrock), is OK. I've done that when the cables aren't long enough. This meets the definition of accessibility.

"We are taking down an extra large square fluorescent light and replacing it with one two-bulb type flush mounted light and maybe another if need be then also adding a pendant over the sink." It will depend on the size and layout of the kitchen. One flush mount will not work as good as the fluorescent for two reasons. (1) The fluorescent puts out 6.5 times as much light. A 4' fluorescent with 4 tubes (2600 Lumens × 4 = 10400 Lumens) A two bulb flush mount w/60 watt bulbs or equivalent (800 Lumens × 2 = 1600 Lumens) (2) The surface mount fixture's light source comes from exactly 2 points that are very close together. The fluorescent light source has infinite sources of light within that 2' × 4' area which spreads the light out better, causing less noticeable shadows. With the fluorescent, the light reflecting off of all the other surfaces in the kitchen is also bouncing off at a more infinite number of angles, (compared to just from the pinpoint light source of the standard fixture) further contributing to the feeling of even light in the kitchen. . Pendant lighting that is bright enough to really contribute to the overall lighting of a room will also be glaring, since it is down closer to eye level. Pendants are fine for specific task lighting or mood lighting. Under cabinet lighting can also be a bit glaring if it is relied upon for more than half the light needed for a task. Keeping the under cabinet lighting out close to the face of the cabinet helps. Using two surface mounted luminaries on the ceiling will help spread out the light sources and help the light bouncing off of the cabinets light the room more evenly. Whether I would use fixtures with two or three bulbs depends on how big the kitchen is, how much light you are used to, and how intricate your tasks are. 800 Lumens × 6 bulbs is still only 4800 lumens, or less than half of what you currently have. You could try taking out two of the tubes and living with it for a while to help decide how many fixtures you want on the ceiling. . The difference between two 3-bulb fixtures and recessed cans over the outside edge of the countertop should not be enough to worry about as long as you have the under cabinet lighting and the pendants. There is a trade off between the two types of lighting. The recessed lights can be put right where you need them, but the light does not spread out as evenly. The surface mount in the middle of the room can produce more unwanted shadows, but the light spreads out and bounces off everything better to counteract the problem.