[1] If God is a temporal entity (which is H&R's position), this means that He is experiencing time in the same manner that we do- in a linear stream that goes from instance to instance. Each moment as it passes becomes the past; each moment yet to be experienced is the future.
What I find a bit harder to swallow is the example given about "Jones" and his awareness "I am thinking." To put it simply, I would expect a God to also be aware that "Jones is thinking"; isn't he supposed to know when "Jones is praying?" There's not much difference...
Maybe what the text is implying is that there is a difference between being aware ourselves, compared to God's knowledge of that same awareness. "I am thinking" and "God knows I am thinking" are not the same (but I daresay close enough).
The most prominent historical argument for compatibility of omniscience and knowing the future (at least as cited by H&R) comes from Luis de Molina...
[2/Part 1] (a lot of ground to cover here...)
Hoffman and Rosenkrantz defend the premise that Jones has no free will in attending the lecture- and "epistemic considerations" is just a fancy way of saying "in a knowledgeable manner." By applying logic to the various premises, it follows that if God is omniscient and has always known Jones would attend the lecture, then Jones has no choice... he will be there.
However, we must remember that Jones, at the very least, lives under the illusion that he makes the choice freely. So, for practical purposes, there's really no conflict in this situation. We, as humans, live our lives under the assumption that we make choices in what we are going to do in any given moment. If this is not actually the case, the illusion is nevertheless so realistic that we cannot know the difference. So it doesn't matter.
We could very well live under all sorts of illusions and never know it. The entire universe and all its history might just be a dream that God is having. Every human that you come in contact with might only be a robot, constructed by God- and you are the only real living person, a subject of a divine experiment. An omnipotent God could easily create any illusion He wishes. But moving on, to the prompts:
"(PEP1) (p entails q, and S has it within his power at t to bring it about that p obtains) ... S has it within his power at t to bring it about that q obtains" (H&R 130).
Okay. Let's get real here, and try to decipher this equation. First, we plug in what the letters (p,q, s, t) stand for:
A possible state of affairs (p) includes the actual state of affairs (q), and an agent (S) that has the power at a particular time (t) to make that possible state of affairs (p) true... Therefore, the agent (S) has the power at a given time (t) to make the actual state of affairs (q) true.
(Not much clearer, is it?) I'll try again, simplifying more:
What might happen is a large set of events; what will actually happen is a singular member of that set- the one event that will happen. God (the agent) has the power, at any given time, to make any of those events that might happen turn out to be the one that will happen.
Rather than going through that lengthy process again for PEP2- (one can plug those same terms in)... The only real difference between them: PEP2 says that the possible state of affairs and the actual state of affairs are the same thing.
What H&R follow with is a string of hypothetical situations (Jones and a red rocket, Jones and blue squares on a sheet of paper...) and other curiosities involving 2+2=4 vs.a rolling ball, or George W. Bush scratching his nose vs.George Washington being the first President. While very interesting as thought experiments, we eventually get to H&R's conclusion- even though God is omniscient, He cannot know how future events, in which there are options, will play out.
[2/Part 2]
"the past is fixed in the sense that it is impossible for us to act so that a fact about the past would not have been a fact about the past."
I am a 55 year-old man, born in 1960, in western NC, to a unique set of parents. I've been married three times, and have a 26 year-old son from the second one. I've played guitar professionally for 40 years... these are some basic facts about my life, from my past, that are true in the present and will always be true in the future. Nothing that I, or even God could do, can change them. (At least as far as we know presently).
How this applies to the God/free will dilemma is simply this: If God had always known that I would be born in 1960, then that is a fact that exists in the past. If my parents actually had any choice in the matter- (maybe they could have decided to wait a few more years to have children...) then that would make a fact about the past (God's knowing my birth date) false- and that is impossible.
These premises can, of course, be tweaked- H&R offer a compromise in which, instead of knowing, God has always believed that I would be born in 1960. This allows for that fact about the past to remain true, right up until the moment for my birth arrives- if for some reason it doesn't happen then, all God has to do is adjust his prediction- His belief that I'd arrive at a certain hour is still true, in that past when He held it.
This is the difference between "bringing it about" (knowing that something will happen) and "acting so that" (believing that something will happen). It is also the essence of the Ockhamist stance between "soft" and "hard" facts about the past/future. If God knows everything that is going to occur in the future, that body of knowledge is hard facts; if God instead only has a strong belief that such will occur, those beliefs are soft facts.
Argument C is, basically: "It is impossible for anyone so to act that a fact about the past would not have been a fact about the past". By adding "soft" into the statement before "fact", the argument becomes invalid.