I am sorry for all that you have gone through, but I a judge is not going to say that cause you saw a title to a video that had the word babies in it that he is a sexual pedifile. Nor can you make false allegations to the police about him being into child porn based on a title with the word babies in it to try to get him in trouble... the courts will look at that as you being petty and vindictive and could possibly give him full custody.
It sucks that he left you... he sucks that he cheated on you... and unless he was charged and found guilty for the alleged assault on a girl 9 years ago... that didn't happen.
You need to just focus on you and your child... hire an attorney and give him the information that you want looked at and if anything can be used, he will but be prepared for your ex to get up to 50% of your child's time.