Neem is effective against mites, and it becomes systemic in the plant after continued application. This means not only are the adult mites being killed by the neem (suffocation from the oil, neem messing with their brains and telling them to stop eating, messing with their molting, ect) but that the plant eventually builds up neem in it's system and the mites die as they eat it. The plant in the picture you showed us with mites is toast. Too far into flower and too many mites to save it now. Personally I'd throw it out, but it's your bud and you should do what you think is best.
As for the caterpillars, man I hate those bastard! Get some mosquito dunks and soak them in some chlorine free water, make sure to keep everything out of direct light. At dusk go spray the plants all overwith the solution. The BT bacteria will infect the cats and kill them all dead. Make sure to do it at dusk or lights out as light (specifically UV) will kill the bacteria before they can get the buggos.
That's all I've got for now, good luck!
