It melted because Rand was a complete n00blet in using saidar, and tried to force it into doing what he was supposed to let it do by itself, which would normally result in the channeler being burnt out and all sorts of destructions happening, but probably because he was the Dragon Reborn and linked to boot, it couldn't happen. When the strain went over the capacity of the sa'angreal to contain, it collapsed.

What? When was it confirmed that Lanfear was severed inside the doorframe ter'angreal? Anyway, since Moridin, Aran'gar and Osan'gar retained the power they had as Ishamael, Balthamel and Aginor respectively, I doubt Lanfear would come out weaker from ressurection "just because". And RJ's statement that being healed from Stilling by a member of the same gender puts that damper to your strength in the Power can explain this, but I miss any confirmation that Lanfear was actually Stilled (much less killed) by Moiraine or the Finn.