Here is what I can remember. Hopefully I can help fill in some gaps
Game 1: The one with three 'F's
The game had three F's that could never be consecutive, and then there was a 'ST' block. Outside of that there were also R's and (I think) L's. Only one of each of them though, so FFF makes three and R S T L makes seven altogether.
The key was getting a couple combinations together and always keeping in mind that F could not be next to another F. I don't know why, but this game actually took me the longest of the four. I think that it was because there were a few different combos and the questions would ask questions about if something is in one spot, then who can/cannot go in another spot #.
Game 2: Dogs
For this game I just took the two dogs that absolutely needed to go together, L and R, and placed them in groups 1, 2, and 3. Starting from there I just followed the different rules to get the different possibilities. There was about two to three possibilities when LR was placed in groups one or three, and then two when the LR block went into group 2.
If you got this, then the questions were MEGA easy and the game lasted maybe 3-6 minutes, depending on your speed in setting it up.
Game 3: Archaeological Sites
From what I remember, it said EACH OF THREE SITES, which to me meant that each of them had to be visited at least once. Don't quote me on this though.
G had to be with 10, and there was only one G. G could go in spot #3 since 10th c. is more recent, and this would mean that both the 1st and 4th sites had to be either 8th or 9th centuries. HOWEVER, we knew that 'O' could not go in #4 (and #5), so that means that if G is in #3, then spot #4 HAD TO be 9th century (otherwise we would have to put 'O' there. I think that this was already mentioned above.
Game 4: Parking Lots
The possible combinations were XYYZZ and XYZZZ. I was not too sure about the question about Z being $12 and so which day would Y need to go. I think that the answer was either Monday or Tuesday.