Is it possible to
1) play units special ability during action phase
Yes, but only if the ability say "Action:" at the beginning. For example, the Storm Sorceress card has an Action ability.
On the other hand, "When Played:" abilities are not Action abilities and can only be triggered in combat. 90% of the abilities in this game are When Played abilities.
2) use units STRENGTH during combat phase
That's pretty much the only time to use a unit's strength.