"Il y a moins de temps que je ne pensais."
The use of "ne" is optional here, does not mean that the sentence is negative, and only there to ensure a smooth flow of the sentence.
If you want to know more about "ne explétif": http://french.about.com/b/2012/11/15/ne-expletif.htm
... before my plane takes off // between my birth and yours // since we last met....
I see. It makes much more sense to me to say "there is less time than I thought (there would be)." I don't think it a good idea to put "I was thinking" as the standard answer.
Yes, it could, but we would rather say "il y a moins longtemps que je ne pensais".