Question 2 is where it gets counterintuitive, and it is worth its own explanation because it feels like a contradiction.
Going down is less metabolically costly: you burn fewer calories per minute than going up, and if you measured oxygen consumption it would be clearly lower. So in the energy-budget sense it is easier, and that matches the intuition that you are releasing energy rather than spending it.
But eccentric contractions are unusually damaging to muscle fibres. Holding a load while lengthening produces more microscopic damage than shortening under the same load. That is why walking downhill for an hour leaves you with sore thighs two days later while walking uphill for an hour leaves you tired the same evening and fine afterwards.
So "tiring" is doing two jobs in your question. Downhill is cheaper in fuel and harder on the tissue. Both are true and they are different currencies.