1)If you invade an empty hex and assault an adjacent port, does the -1 for amphibious assault and +2 from naval support still apply to the battle?
So long as the port is a coastal hex, the +2 DRM applies. (See CRT: +2 Naval Support, attacking a unit in coastal hex affected by Fair weather)
However, the port has to be adjacent to the sea zone where the surprise marker was placed. For example, you can't invade Sardinia hex 4221 (sea zone 20) because the only adjacent port is Cagliari, which is in sea zone 19. Rule 6.3.2, Amphibious Invasion: the invaded hex must be in a Sea Zone containing a friendly Surprise Attack marker, and if the invaded hex has no port, at least one adjacent port must also be in that same Sea Zone.
The -1 DRM applies if the invading unit attacks, whether coastal hex or not.
2)If an escorting fleet was reduced to -6 sorties from an interception, but the convoy was not interdicted, would the fleet still add naval support to the assault?
[edit: Corrected the answer based on Sal's response in another thread.] Nope, the +2 DRM does not apply if the escorting unit has six sorties. 5.3.4 Amphibious Invasion Assault: If an Assault is fought in a coastal hex as part of an Amphibious Invasion (6.3.2) and an escorting warship unit or Surface Action marker with less than 6 Sorties is in the invading force, the attacker applies the Naval Support DRM. The defending hex does not have to be the invaded hex.