I've made some basic observations above, but here are some others...
Have I correctly identified 14 different sentence patterns? Or is the passive voice a separate entity not to be included? In which case there are 8 sentence patterns.
Well, your original sentences can be made into questions...I gave a book to Peter? To Peter I gave a book? etc.
Also, there are two form of the passive: static and dynamic (http://en.wikipedia.org/wiki/Grammatical_voice#Dynamic_and_static_passive), so each of your passive sentences can be modified by inserting the word 'being' before given. The difference in sense is one of greater 'activity', a sense of something being pictured as happening or in progress.
Which sentence or sequence of words are incorrect and why?
3, 6, 11, 14 seem wrong. I cannot imagine a native English speaker using #3 except by mistake, or perhaps in poetry in order to meet the metrical demands of the line. With the verb 'give' you can only do #1. #3 is the sort of thing I can picture myself hearing foreign language learners saying. You cannot invert the direct object and indirect object after the subject without dropping 'to.' This is the same with the verbs offer or send. Some verbs, like report, can't even do the inversion in the first place.
Do these patterns have names?
And please share any interesting or curious grammar facts which I may have overlooked in my question.
The examples in 1 through 9 that do not begin with the subject (i.e., I) are called 'inversions.' Inversion is a technique for changing the focus of the sentence. Focus, as a grammatical phenomenon, was largely ignored by traditional linguistics, but has become of great interest to today's linguists (http://en.wikipedia.org/wiki/Focus_(linguistics))
Besides changing the focus of the sentence, these inversions also serve poetic purposes. In florid and formal writing, they provide variety, and they provide an additional way to meet the demands of the meter.
Note that sometimes inversion is grammatically required. For example, the place of "Had" cannot be changed in "Had I given Peter the book, he would have known what to do." -- unless the whole sentence is restructured: "If I had given Peter the book, he would have know what to do."
Finally, the remaining examples in the passive have their own 'feeling' to them. Although the passive is much more common in English than in many other languages, the effect of using the passive is to diminish attention to the agent (the person/thing doing the action) in favor of the person/thing being acted upon (the patient, in Latin). Much has been said about this. (http://en.wikipedia.org/wiki/English_passive_voice#Style_advice)