if my opponent activates premature burial and i use herald of the green light to negate the activation of it does my opponent still have to pay the 800 since i negated the activation of the card?

the 800 LP is a cost to activate it....he payed the cost as soon as he played it...even if your were to negate with a card like solemn judgement...he wouldnt get his LP back.

Costs are always paid before a card is actually activated for you to chain to and are never refunded if negated.

probably an easy way to view it is that when you activate a card, you pay the cost to put it on the chain block. A counter, or chaining effect, cannot do so UNTIL the first card is put on the chain block. By then the cost was paid, and even if the activation and effect were negated, the cost is lost to the player forever.