Half-Levels only provide the opportunity to go Hull-Down. They are otherwise the same as a terrain a half-level below.
1. Partial-Cover, because the underlying terrain is 1 lvl high.
2. No, because a BattleMech cannot change levels by more than 2 per hex.
3. That's what the chart on pg. 30 of TO:AR says.
4. No, because the Intentional Fall from Above rules modify the Accidental Fall From Above rules, which preclude falls of 1 level or less.
5. As an optional rule, players can decide whether the half-levels may be maintained by a VTOL or not, but as there is no benefit to not simply rising full levels that's a lot of extra book-keeping to take on for no real advantage.
6. WIGEs cannot gain elevation, only maintain it. Ergo, they may choose to remain a half-level off the underlying terrain after moving out of a half-level hex, but the cost is inefficient.
7. No