LOST (Warning: Possible Spoilers)

[onlydarksets]

That might address #1:
Before Desmond travelled to the past, the "present" Danny didn't know who he was. After the moment in the present when Desmond went back and made contact with "past" Danny, "present" Danny seemed to remember him (at least, his journal did).

Assuming actions in the past actually happen concurrently with the present (that is, there is a moment in the present when someone goes into the past, and that is the moment when the timeline changes, as opposed to the timeline changing the memories of people in the present from the moment the past action occurred), that would explain the inconsistencies.

That is, Desmond did communicate with Penny up until 3 years ago. However, when he went into the past, he changed all of that by telling her he would take 8 years to contact her. Of course, that begs the question why he did the race if he wasn't trying to get her dad to leave them alone.

For #2, though, I don't think that addresses it. How can minutes go by like hours, but days are the same?