1. Regarding Electra, tonight my friend played her and she was the only one on his side. She was injured after I attacked and then on my friend's turn, before Electra attacks, she can heal one damage on one of your units, can he heal Electra herself?
If she is one of your active units, then yes.
2. Another situation that appeared was Atalanta in Olympus and Hector in Troy on opposing sides. Atalanta does not take damage from blue cards and Hector, a multicoloured card, inflicts one damage on every enemy unit before attacking. In the rules is says, "Effects of special abilities that affect a specific color ALWAYS affect multicoloured Heroes." Does that mean that Atalanta can't be attacked by any of the multicoloured heroes as well as blue cards or do the rules imply that when someone is attacking a specific colour it applies to the multicoloured heroes?
Thanks in advance!
Multi-colored cards count as all colors. So, Atalanta is immune from damage from blue cards and every other multi-colored card, as they count as being blue/red/yellow/green at the same time.