Especially about Finns weapon.
If I use that weapon and Cheap Shot or Stunning Blow. When do I check if the enemy is engaged with me? At the start of the test or before I apply damage?
When I read the card I somehow get the feeling it is at the start of the test but I would like to know from more experienced players.

you can't use cheap shot and finn's gun together, they are both actions.

as for stunning blow, you check whether the test is successful before applying effects, so you can get the extra damage since the enemy is evaded immediately on success.

Ah, my bad on cheap shot but thank you for the clarification.
Not that I am sure when it would apply since Finn have an extra evade only action but good to know regardless.

finn's extra evade action is also still an action, not a reaction or skill effect. when you declare an action, you cannot pool other actions into it; you can only play reactions and/or fast cards to it if triggers are satisfied or skill cards/symbols during the test the action creates.

Finn's evade action is a use of any action keyword Evade: and it doesn't take up one of the 3 actions you are provided during your turn.