Online Rules Reference reads;

"1. After an enemy card is revealed, it is added to the staging area.
2. Enemy cards remain in play until they are defeated or removed from play by a card ability.
3. If an enemy engages a player, it remains engaged with that player until it is defeated or removed from that player’s play area by a card ability.
4. When an enemy enters a player’s play area from another game location, that enemy has engaged that
player, and that player has engaged that enemy.
5. An engaged enemy does not contribute its threat strength to the total threat strength of the staging
area.
6. Instead, each engaged enemy makes an attack during the combat phase.
7. An engaged enemy remains engaged with a player until it is destroyed, moved to another play area, or
removed from play."

Now my questions (I was very confused on these points and I see I was playing it wrong. So it's important for me to clarify these points 100%. Thanks for bearing with me!);

a) Number 3, 5 and 7 are valid regardless if the player engages the enemy or the other way around; the enemy engages the player, right?
b) What time length does the number 7 above refer to? Will it will remain engaged (and won't contribute to the threat count, and will remain in player's play area unless a game effect moves it somewhere else) until the end of the phase, round or the game, if it isn't destroyed/removed/moved by then?
c) An enemy engages with a player, not with a character, right? Does this means, if an enemy attacked a character in a specific phase, it doesn't have to attack again same character in another phase/round, right?
d) Is there any difference between a player attacks an enemy and an enemy attack a player?

More will come about some other, related points after your responses.

3 hours ago, mrblue74 said:

a) Number 3, 5 and 7 are valid regardless if the player engages the enemy or the other way around; the enemy engages the player, rig  ht?
b) What time len  gth does the number 7 above refer to? Will it will remain engaged (and won't contribute to the threat count, and will remain in player's play area unless a game effect moves it somewhere else) until the end of the phase, round  o  r the game, if it isn't destroyed  /removed/moved by then? 
c) An enemy engages with a player, not with a character, right? Does this m  eans, if an enemy attacked a character in a specific phase, it doesn't have to attack again same character in another phase/round, right? 
d) Is there any difference between  a player attacks an enemy and an enemy attack a player?  

a) Yes, if you engage an enemy, the enemy engages you, and vice-versa.

b) An enemy is engaged until the end of the time, or it is removed from being engaged somehow - either by being destroyed, moved back to the staging area, etc.

c) Yes, you can imagine that there is an area between that staging area and your cards that is "enemies engaged with you". They stay there, not contributing threat to the staging area. They are engaged with you as a player, not with a specific character, so they can attack different characters on the next round.

d) If you mean "engages", then no, not really. If you mean attacks, then yes - it's sometimes possible to attack without engaging. Some cards have effects that will cause an attack without engagement, for example attacking an enemy in the staging area. But that's card-dependent.

8 minutes ago, icabod said:

b) An enemy is engaged until the end of the time, ...

What do you mean by “end of the time “? End of the round if it doesn’t get destroyed or removed? End of the game?

Thank for other parts of your answer!

He means until the game ends and you stop playing to put the cards away.

Indeed, sorry. Yes, it's engaged until the end of the game, or it becomes disengaged - by being destroyed or a card effect.

Worth noting that you can't choose on a whim to disengage an enemy and return it to the staging area. It has to be by a card effect, such as A light in the dark .

Ways that an enemy engaged with you becomes no longer engaged:

1) You destroy the enemy

2) A card effect causes the enemy to be engaged with a different player (example -- another player's Tactics Aragorn steals your enemy)

3) A card effect causes the enemy to be returned to the staging area (example -- you use Ithilien Archer's response to return an enemy to staging)

4) A card effect causes the enemy to be put out of play (example -- finishing a quest stage directs certain enemies be put out play.)

5) You are removed from the game (example -- you threat out in a multi-player game, enemies engaged with you are return to staging)

And each enemy who is still alive will attack my characters once every Combat Phase as long as he is alive, right?

Unless there is a card effect preventing it (for example, Feint or Forest Snare), each engaged enemy will declare an attack on you, the player, each combat phase. A ready character may be declared as a defender, either one of your characters or another player's sentinel characters. If a defender is not declared, the attack is undefended and the damage will be placed on one of your heroes.

We can declare only one single defender per enemy attack, right? Not more than one defenders for same enemy who attacks?

Absent some card effect (like Stand Together from the core set) you can only declare one character as a defender. You can combine characters on attack.

Thank you very much for your answers and I am so sorry for so many questions about only a few points left .

What I understand is only difference between optional engagement and engaging with engagement check is latter is mandatory and former ignores threat cost/dial. Nothing changes in combat phase regardless an enemy engaged with optional or mandatory engagement. Optional engagement simply gives you a choice to engage an enemy who normally can’t attack you yet. Correct?

9 minutes ago, mrblue74 said:

Thank you very much for your answers and I am so sorry for so many questions about only a few points left .

What I understand is only differe  nce between optional engagement and engaging with engagement check is latter is mandatory and former ignores threat cost/dial. Nothing changes in combat phase regardless an enemy engaged with optional or mandatory engagement. Optional engagement simply gives you a choice to engage an enemy who normally can’t attack you yet. Correct?

Correct.

It also enables you to make sure the best player gets the enemy engaged with them in multiplayer. In a 2-4 player game towards the end when even the lower threat decks are at 35+ threat, it can be tricky to make sure the non-combat focused decks don't get an unwanted enemy without optionally engaging.