Ex1 has no rights and isn't on the birth certificate
Ex2 has no rights and isn't on the birth certificate
Therefore you can do a step parental responsibility form with your partner when you are married not before.
You won't need permission off ex1 because although he is the biological father he doesn't not have parental rights nor is he on the birth certificate, and no contact so no child arrangements order.
I've completed one recently, only those with parental rights fill out the form. You can find it easily online, take it to the court to witness your signatures and take photo id and birth certificate and marriage certificate.
I would wait until you have been married a year or two, make sure this relationship is going to last it sounds like you have jumped one relationship to the other.
I thought I knew my ex, knew him all my life then he abused me when I was pregnant and our child once he was born, and sexually attacked me three times. I'm not saying that will happen to you, I'm saying people can hide who they really are or change and relationships can change too, as you know with two exes.
Congrats on the wedding, hope it works out.