As for Giles' spontaneous laughter, I think it made perfect sense. Think back (or re-watch if you were so inclined to tape this one) to what Buffy tells Giles. She sounded like a child, the way she told him how, since he had left, it had all gotten so screwed up, and how Willow went cold turkey, and Dawn's been stealing, and she worked at the double meat palace, and how she slept with Spike, etc. etc. She was coming apart with all these bad things, and he was beside himself with laughter over how what she was describing was no different from the squabbles that we all go through.
It's kind of like how your college-age teenager goes off into the real world, and you come over to visit, and your child tells you how much people hate them, and how much it costs to fix the refridgerator, and how surprised they are that the GOVERNMENT CHARGES YOU for owning a CAR, and how much utility bills cost, and how much the baby cries at night, etc. etc. It touches a reaction deep inside you about how far they've come, how far they have to go, and how much of your little baby they still are, no matter what. It just struck him a ludicrous and adorable at the same time. Parents do that kind of thing - their kids make them laugh all the time; some just don't show it as much.