The RX100 appears to be able to be used with the F43....it does have a hotshoe. However, I don't know how it would fell with that size flash on a small camera like that. It might be worth a trip to a local camera shop and try one out before you order it. Depending on what your are using the flash for you might be interested in the HVL-F20.
The answer is Yes and No. It will connect and fire, but not all the features will be available. Here is a compatibility chart for the flash from Sony. http://www.sony-asia.com/support/resources/en_AP/html/Compatibility/DSLR/Flash/sony/F43AM.html
Yes it does, according to Sony's Web Site. If you have the DSLR-A230Y or DSLR-A230L the compatibility Tab shows this flash.
Note I really like this Flash. I have the A55 and it can keep up in 10 frames/second burst mode for 2 or 3 seconds. Its much better than the little brother flash, which was useless. Good luck
Yes, but the nex 6 has a standard hot shoe so you will need the hot shoe adapter from sony. The a99 comes with the adapter but I'm not sure if the 6 does. You also have the hvl-60 that's made for the new shoeo