Since no one has taken a crack at it and it's been a few days, here's the solution the the string riddle.

You light one string at both ends and the other string at one end simultaneously. Since the total burn time will be 60 minutes, even if it doesn't burn at a consistent rate, the string that you lit at both ends will burn for exactly 30 minutes.

Once the rope lit at both end burns through, the rope you lit at one end will be half-way through it's burn time-wise, if not length wise (the remaining half time-wise could be any length), so you light that rope at the unlit end, cutting it's remaining 30 minutes of burn time exactly in half to 15 minutes.

So you have 30 minutes from the rope you lit at both ends simultaneously plus 15 minutes from the second rope you started at one end, then lit at the other once the first was finished for a total measurement of exactly 45 minutes.