(B) There are a couple of books about open source license that explain the various bits pretty well -- you might want to read them, too.
(C) On your first question, no that's not allowed by the GPL. You've created a derivative work and it must remain GPL'd.
(D) Your "new functions", if they are truly your own independent creations can potentially be separated out into their own e.g., library and you can release just that under whatever license you like.
(E) In terms of your second question, that depends on what you mean by "new source code". If you mean "only the completely new source code that you've written independently" then yes as long as you don't include that code as an integral part of GPL'd code in creating a derivative work. The other cases have been covered above.
(F) IANAL. Seek competent, professional legal advice.
(B) There are a couple of books about open source license that explain the various bits pretty well -- you might want to read them, too.
(C) On your first question, no that's not allowed by the GPL. You've created a derivative work and it must remain GPL'd.
(D) Your "new functions", if they are truly your own independent creations can potentially be separated out into their own e.g., library and you can release just that under whatever license you like.
(E) In terms of your second question, that depends on what you mean by "new source code". If you mean "only the completely new source code that you've written independently" then yes as long as you don't include that code as an integral part of GPL'd code in creating a derivative work. The other cases have been covered above.
(F) IANAL. Seek competent, professional legal advice.