Question 1: Carbonation and Conditioning are SLOWER at lower temperatures, but CLEANER. At higher temps, carb and conditioning go faster, but are not as clean. What you are tasting in the hotter sample is a beer that's more well conditioned, therefore it seems to be better than the colder sample, but really the colder sample is just still at an earlier stage of carb and conditioning, so you aren't comparing apples to apples. If you were to compare the colder sample further down the line at the same stage of carb and conditioning, it would be better than the other sample.
70F is the ideal temp to carb/condition that is a good balance between speed and clean conditioning. If you can't hit 70, it would be better to lower at the 68F than higher at the 80F. At 68F it is going to take slightly longer to carb and condition, but it will be cleaner and you'll end up with a better final product. At 68F, expect a good 15-21 days to fully carb an average gravity beer (OG of 1.04-1.06).
Anything else, more ABV = longer to carb/condition, Less ABV = less time to carb/condition.
QUESTION 2: The sediment technically INCREASES slightly from start to finish. The yeast that are carbing and conditioning your beer propogate/reproduce as they devour the sugars and produce CO2, so there are millions MORE of them at the end of the process than at the beginning of the process. HOWEVER, what you are describing is that there is more sediment IN SUSPENSION that falls out and settles on the bottom over time, so the beer itself will have less sediment in suspension at the end of carb/condition.
That's what you're experiencing. Hope that helps!
Primary #1 - Midnight Ryeder (Midnight Wheat and Rye)
Primary #2 - Florida Weiss
Primary #3 - Kane-DOH APA (Honey Citra APA)
Secondary #1 - Downtown Flanders Brown (brewed August 2012)
Keg #1 - Raspberry Florida Weiss
Keg #2 - Cinnamon Raisin Cider
Keg #3 - NONE!
Bottled - NONE!