(1) What would be the recommended placement for the ceiling speakers in a kitchen which is rectangular with an island in the center and otherwise symmetrical. The office is off to the side.
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................|office.|
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| kitchen..............|
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|...S...|____|....S...|
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There is no real 'ideal' placement of a stereo source when you don't have any obvious 'stereo' seating position. I would likely put one on either side of the kitchen. (denoted by 'S' above) as a baseline recommendation. You really aren't getting top notch sound, but solid fill sound out of this type of speaker setup, and with decent speakers, they will work quite nicely.
The option would be to place two bookshelf speakers at one end of the kitchen, perhaps up on top of the cabinets, but this is if you plan to be a bit more critical of the stereo source - and likely would not deliver much audio to the office.
(2) Since it appears the zone 2 has only left and right speaker output, should I just stick with 2 speakers OR CAN I GET FANCY and have like 4 speakers on each corner with a BASS (obviously this will influence my question in (1)).
You can run 4 speakers off the Denon if you want, but your investment in speakers needs to be appropriate and you shouldn't short change the speakers just to add more of them. I would instead stick with two decent speakers over four cheap speakers.
I am assuming you are running 5.1 in your living room and still have 2 open channels of amplification in the Denon.
(3) Considering the setup you suggest what are some good models for speakers, (I would be looking at low-mid level pricing).
I'm not sure what you consider low-mid level pricing, but there are tons of in-ceiling models out there. To fill a room without a sub, and with hard surfaces, I often recommend the Sonance 831 speakers, which give a 3-way design including 8", 4", and tweeters, all of which can be aimed. It gives you a better low end without a sub, while keeping it all in the ceiling.
(4) ASIDE: I have a small tv in the kitchen (denoted with 'x' in the picture) which is connected to a DirectTv receiver (independent of Denon receiver). Is there a way to use the ceiling speakers for this TV's sound? Would I somehow have to connect the DirectTV receiver to the Denon in my living room OR could I extend the Denon Reciever somehow to the kitchen so I can control the TV and music from the kitchen?
You would need to connect the audio from the DirecTV to the Denon. I would relocate the receiver, make sure that you have decent wiring to your TV in the kitchen, then run analog audio so you can hear it in the kitchen.
I know in my home we only use two cable boxes to feed 4+ destinations for video, and many more for audio. What I haven't checked is if we can output 480i video over coax to a kitchen display so we can add a small TV in the kitchen to augment the display in the family room. But, it's a nifty way to do things.