"Your opponent must subtract 1 from their hit rolls for attacks that target this unit. In addition, add 2 to saving throws made for models from this unit that are in cover, instead of 1."
Thats the rule. They dont add 1 to armor save when the unit is "in cover". They add 2 instead of 1.
To answer your questions.
1. No. When an enemy unit ignores cover, they dont add 2 to their saving throws.
2. No. No one gets cover in
CC. Unless there is a special rule saying so.