Those situations where Talaaq takes place

Husband replying "Fine, take it" when the wife asks him for divorce

Q: After asking my husband for talaaq for the umpteenth time (because of consistent pathological lying, not giving any of my rights as a wife, not respecting me, tarnishing my reputation with his friends and mistresses, giving his first wife a comfortable life and not even giving me any of my expenses, mentally and financially abusing me, etc.) yesterday he finally said "Fine, take it (the talaaq)". Prior to that we didnt have any relationship for the last 8 months. Afterwards when I asked him to give me talaaq in front of my parents, he is saying he will give it when the time is right, and knowing him, he will always find excuses since he doesn't wish me to move on with my life and he wants to have full control over our son (though he hardly pays for the latter's expenses), that's the only reason he doesn't want to give me talaaq. I want to know if the talaaq he gave in the first instance is valid. 

Husband signing divorce letter

Q: In a heated argument with my husband, I wrote out a letter of divorce stating that he (his name) hereby issues me (my name) with a divorce and forced him to sign under his name. He signed in anger of what I was asking. I know that this is wrong. I would like to know if it constitutes to a divorce as I do not want to live in sin.