1 Is it possible to determine the direction of take off (or landing) and runway to be used for an upcoming flight that you're on?

2 If you can, how do you do it?

3 How early can you find out?

1: Not 100%, no. But close depending upon the airport.

2: Take off will always be into the prevailing wind. Beacuse most locations have winds in the same general direction the majority of the time, take offs will tend to be that direction. Some airports vary, but not much. In the absence of wind, take offs will generally adhere to noise abatement restrictions. PHX is unique. In the absence of wind (although generally west to east) they will reverse take off directions based on the time of day due to some contract between Phoenix and Tempe. SAN and LAX will almost always be toward the ocean, except during Santa Ana winds, usually in the fall. LAS is usually east to west, but has less predictable wind directions and will often move that to northerly take offs. ORD is a crapshoot. LHR will generally take off westerly.

3: Depends on the general airport, but given unsual weather you can find out that day.