A card stays in control of its player as long as it remains on that player's arena face up. That means whenever a player summons a unit or builds a construct, they will control that card until it leaves their arena or is no longer face up. When a chant or response card is played, it enters the arena and leaves upon its resolution, meaning it will also be in control of its player during that frame.
It refers only to this specific card, rather than all cards with that name.
No. Such effect consists of multiple instances and each has to be resolved 1 by 1. It means players will get to respond to each instance separately and cards such as Barrier of the Mind will only affect the specific instance of an effect that they are responding to.
All and only face up cards cover, regardless of their status. A face down card cannot cover.
Those 3 can be considered different stages of the same action. Firstly, when you declare an attack during your battle phase, players have a window to respond to that declaration. If the attack is negated with effects such as Defensive Stance, it will not happen. However, the declaration was already made, so the exhausted status remains on the card that made it and it cannot declare an attack again unless that status is removed. On the other hand, if the attack is not negated, it progresses to damage calculation step, where players have one more opportunity to respond. The base damage dealt is the current ATK of the card that is declaring the attack, but all effects affecting combat damage have to be taken into account as well. If at the end of the calculation the total damage comes out as positive, the attacking card is considered to have dealt combat damage and on-hit effects are applied.
Healing restores card's current HP up to its maximum HP, while gaining HP increases both current and maximum HP.
Combat damage is any kind of damage delt by a card on either player's arena during the battle phase.
In that case, both cards deal damage to each other at the same time.