1) All four sentences, whether they use 'down' or 'up' are correct. In my experience, 'to' is more common and natural than 'for'. As far as 'down' and 'up' are concerned, 'down' is, at least for now, mostly used by young adults, whereas 'up' is not as age-specific.
2) The second sentence is correct. Note that because "your pity" is not a complete clause, you do not need to place a comma before 'nor' in the first sentence. The reason the first sentence is wrong is because it is a double negative; the "don't" applies to both "your help" and "nor your pity", which technically means the speaker does need your pity. However, it's not unnatural to hear double negatives in common speech. You may also phrase this statement as, "I need neither your help nor your pity."
3) This is actually quite a difficult sentence to parse, even for a native speaker. We can break it down into what each piece is trying to describe... First of all, we have the main meaning of the second sentence:
"There is talk of the Dauphin's men in all their gathered hordes and a reckoning soon to come."
"tracked on their track" and "at terrible odds" each describe the thing before them.
"tracked on their track" most likely means, in this context, that the Dauphin's men are following the tracks of the men who are marching in the first sentence.
"at terrible odds" describes the reckoning. Given the threat of the Dauphin's men, the reckoning is likely for the men who are marching in the first sentence. It comes at terrible odds, which implies that they are unlikely to survive. "terrible odds" just means a low chance of victory. When gambling, people often talk about the odds of winning, for example.
Often with older texts, it is difficult to discern the exact meaning. I'm sure we've all had our share of literature classes!