Interview Maths Puzzle Numerical Ability

I have a box of one hour fuses. If I set one end of a fuse on fire, I know that the fuse will burn all the way to the other end in EXACTLY one hour. However, the fuses may burn unevenly [ie - it may take 59 minutes to burn the first half of a fuse, but only 1 minute to burn the other half]. Furthermore, all of the fuses may burn unevenly at a different rate. The only thing we know for sure is that each one takes 1 HOUR to burn completely. The Question: Given 2 of these fuses and a lighter, how can I time out 45 minutes precisely?

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There is a building of 100 floors If an egg drops from the Nth floor or above it will break If it’s dropped from any floor below, it will not break You’re given 2 eggs Find N, while minimizing the number of drops for the worst case.
 A rectangular room measures 7.5 meters in length and 3 meters in width. The room has a height of 3 meters. A spider sits 25 centimeters down from the ceiling at the middle of one of the short walls. A sleeping fly sits 25 centimeters up from the floor at the middle of the opposite wall. The spider wants to walk (i.e., move along the walls, floor, and ceiling only) to the fly to catch it. How can the spider reach the fly, walking just 10 meters? Is it even possible?