Hi.

Lord Alcaron have the text: " Forced: When Lord Alcaron is dealt a shadow card with no shadow effect, he makes an additional attack after this one (deal and resolve another shadow card)."

1) If the first shadow card have no shadow effect then Lord Alcaron makes an additional attack. But if the second shadow card have no shadow effect too, will he make third attack and etc?

2) For an additional (second) attack, the number of shadow cards will be two - one of the first attack, and one of the second attack, or only one - of the second attack?

1) Yes he will

2) The first shadow card doesn't affect the second attack unless it has an "until the end of the phase" effect.

When an enemy makes an additional attack you discard the old shadow card(s) before dealing a new one.