Is the custody and visitation arrangement court ordered or a casual arrangement between the two of you?
If not court ordered, you should ask the solicitor how to go a out getting it ordered by family court, what the advantages of that are.
You should ask the solicitor about maintenance. Why is he not paying any?
Have you ever done the Women's Aid Freedom Programme?
You seem to be very afraid of this man. Please understand that if he has a tendency to engage in displays of rage or displays of disrespect for agreements, there is nothing you can do to stop any of that. If he goes too far, makes threats, harasses you, you can call the police.
If he wants birth certs he can get his own copies and pay any associated fees. You don't have to hand them over. You don't need an excuse not to hand them over. You don't have to tell him how he can get his own copies either. You are not his secretary.
I would seriously advise you to tell him you will only respond to communication from him by email in future. No more phone calls where he can deny everything he says.
You need to start pushing back and stop letting him use your children as pawns in his ongoing fight with you or as a way to increase his income.