1. The card Direct Hit says resolve one of your dice showing ranged or melee damage, increasing its value by 2. If I had a die showing a matching modifer to that damage type, can I resolve that then, too?

2. When a die says 2 shields, do I have to give both to the same character or can I give 1 shield to 2 different characters?

1. The keyword there is 'one' - "resolve one of your dice" means you can only resolve one die. No like symbols. No modifiers.

2. Generally you can only give shields from dice resolutions to one character, although the card Diplomatic Immunity lets you split the shields between different characters.

Resolving dice through a card effect follows all the normal rules of resolving dice unless otherwise stated. You can resolve a a dice alongside a modifier if you are able to resolve more than one dice (e.g. Maz's effect). But yeah, anything that lets you resolve one dice means no modifiers.

Shields can't be split (again, unless otherwise stated). However it's important to remember that you actually resolve dice one at a time (ignoring modifiers); so if you've got two dice with one shield each, you could give the shields to two different characters.