As Thought Gorger's first ability resolves, putting a +1/+1 counter on it for each card in your hand is mandatory. The effect says "if you do" because performing that action might be impossible. If Thought Gorger has left the battlefield by the time the ability resolves, you can't put any +1/+1 counters on it, so you won't discard your hand.

Once an ability starts to resolve, it's too late to respond to it. For example, you can't count a card in your hand while determining how many +1/+1 counters Thought Gorger gets and then cast it in response. If a card is counted, it'll be discarded.

When Thought Gorger's second ability resolves, its last existence on the battlefield is checked to see how many +1/+1 counters it had on it. All of them are counted, not just the ones put on it by its "enters" ability.