6.4.1, due on October 25

1. (Difficult) This section seemed pretty straight forward and understandable.  It seems like it focused more on the technique of the quadratic sieve, and less on the theory or proof behind it.  I am a little confused on why it works.  I also wonder if there is a good, general-purpose method of choosing the parameters for attempting to generate the squares?  I didn't follow all the math or look at all the numbers, but hope I could figure it out if needed to for a homework.
2. (Reflective) I wish that this section had talked a little more about how likely it is to find factors using this method, and how much more likely it is than other methods we've discussed.  It is interesting that a 200-digit number was able to factored.  Isn't 1024-bits common for RSA?  It looks like 2^1024 is a 309 digit number.  Looking at the growth in factorization records over the years, it would seem this may be possible in the not-distant future.  Is there something I'm not understanding that would lead people to believe 1024-bits is safe?  Maybe that's not really the current practice or recommendation.  Maye getting that 200 digits took and extraordinary amount of effort and computation, and factoring far fewer digits is still not generally achievable?  Maybe it was a special 200 digit number?