Is there an intrinsic "right and wrong" or moral code that would exist whether or not there was a God?
No. Moral codes are cultural artifacts, except for incest taboos, which are pretty universal as regards incest in the first or second degree. Incest seems to be rooted in biological disinclination as much as socialisation to a certain culture's morals. Kids raised together between certain ages are very unlikely to find each other sexually attractive, even if unrelated.
Apart from that, it would appear there is not an absolute or universal moral code.
There are high degrees of agreement between cultures on certain wrongs; murder and theft (where property exists), for example. These commonalities are largely understandable as implicit reciprocal agreements between people in the same society; you no kill me no steal my spear I no kill you no steal your spear. Not so much morals, as enlightened self-interest.
But the differences in moral codes between cultures are greater than the similarities, although, to be fair, the similarities are often those with the greatest impact on day-to-day life.
For example, with something as Universal as sexuality (between non-related partners) morals vary wildly. In many parts of the world at various points a 14 year-old bride would not be considered odd or wrong even. Now it would be considered illegal and wrong - in most parts of the world. Most, if not all cultures have something corresponding to marriage, but they vary from codified forms of passing property on to decendants to exclusive contracts of sexual faithfullness and breeding exlusivity.
To put it another way, is what we believe is "right or wrong" based on whatever God decides is right or wrong (ie. he set's the standard) or is it an intrinisc thing that he also must adhere to in order to be thought of as 'good'.
Moral codes are set up by socialisation. Witch burners and Khymer Rouge re-educators both think of themselves as doing right. If any god applied seperate rules to themselves and their creation, most people would regard it as immoral, as most cultures I have had contact with dislike double standards.
If God has to adhere and go along with some intrinsic value system then does this effect any claims to be omnipotent and always good? ie. can he do certain things or go against this set of values.
The values an individual would use in assessing the morality of a god would vary according to their society. Most Christians would think Quezlecotal (sp?) an immoral god, but Aztecs wouldn't. This would mean that a lot of a god's actions would be viewed as moral by some humans and immoral by others. If one postulates ONE god, then the cultural differences still exist, thus the differences in opinion about god's morality. This causes some logical problems is you allow the number of gods in the equation to equal 1.
If it's the opposite and whatever he decides is good or bad actually becomes 'good and bad' for us then where does this leave our free will? If 'fight and maime' for instance became the right thing to do, would our objecting to do it make us bad and evil?
In such a scenario, freewill would not be freewill, and Satan is very probably a freedom fighter, slandered by the propoganda of a totalitarian despot. As for morals varying under certain circumstances, that's just human nature. I'm non-violent but would happily wade through other peoples' blood to keep me and mine safe, and see this view as very moral.