So if you plead not guilty to some crime, and they find you guilty, do you get prosecuted for lying in court with your plead as well as for the original crime?
I believe that entering a plea doesn't count as testimony, thus isnt subject to perjury laws. Most of my cases were plea deals before trial, or were cases where the defendant did not testify. Saying "not guilty" also doesn't necessarily mean you didn't do anything, you may honestly believe at that point, and make the argument, that the thing you did was not illegal.
What about Alford pleas? I thought they existed so that you could reserve the right to appeal or avoid a civil action by avoiding an admission of guilt while acknowledging that you will likely be convicted.
IANAL but from what my lawyer friends have told me an Alford plea is practically the same as a guilty plea for purposes of appeal. In other words, it's very difficult to appeal an Alford plea. Seek legal advice before considering an Alford plea.