To activate the last ability, there must be a legal target: a spell on the stack. That target will determine the value of X and the mana value of the card you discard. You can't activate the ability unless you can match the mana value of a spell on the stack to that of a card in your hand.

The mana value of a spell doesn't change, even if it's been cast using an alternative cost (such as an awaken cost). For example, the mana value of a Sheer Drop (a spell with mana cost {2}{W}) that's been cast for its awaken cost of {5}{W} is 3.

If there's an {X} in the mana cost of the card you discard, that X is 0. Any {X} in the mana cost of the target spell will have whatever value was determined for it as the spell was cast.

Kozilek's triggered ability checks to see if you have fewer than seven cards in hand when you cast it. Kozilek is on the stack at this time and not in your hand. If you don't, the ability won't trigger at all. If the ability does trigger, it will check again as it tries to resolve. If you have seven or more cards in hand at that time, the ability won't do anything.