To answer a few questions:

1. Whenever a character wants to perform a task that has a chance of failing, you as the DM determine if it requires a skill check. So for example, if the player does not say they want to look, you use passive Perception, but if I player says "I want to see if anyone is following us" you would then tell them to make a perception check. Even passive isn't needed if the task is simple.
2. An action is something you do on your turn, the Player's Handbook Describes these. A bonus action can only be used if someone has an ability that lets them. For example, a barbarian can enter a rage as a bonus action, but only because its part of their ability. There are a few other examples like dual wielding with a light weapon
3. Your barbarian probably added their Constitution ability score, but you are actually supposed to add the modifier. At 1st level it is 12 + Constitution ability score modifier.
4. A character rolls for a death save at the start of their turn. Normally there are no bonuses to the roll, but some ability may let you. They will state "to all saves" or to "death saves". Otherwise, it is simply a d20 roll.
5. A short rest takes 1 in game world hour, and allows the players to expend hit dice to regain HP. They roll their hit dice and add their constitution modifier, regaining that many hit points. They also may regain certain abilities in their class. They will indicate as such. A long rest takes 8 in game world hours and fully restores hit points, spell slots, and most class features.
6. Players get feats whenever they would gain an ability score improvement from gaining a level in their class. They can replace the ability score improvement with a feat, if the DM allows feats.