Heard that unicorn is one of the most powerful level 3 unit.

So how do you recruit unicorn?

Is taming it during exploring the only way to recruit unicorn?

How can you tame a unicorn successfully?

Are there any conditions you need to meet to increase success rate of taming?

I encountered this event a few times but never managed to tame it with success.

Only during this encounter. You can find him only in forest.
To tame him you need positive karma, probability 30%/(100-diplomacy*10). With diplomacy 5 level probability 60%, without - 30%.

Anyway, I think minotaur would be better. Neutral+round attack.