So i'm not a lawyer but I went from the same sort of thing from your ex's side and had spoken to a lawyer and got advice.
We had to send each other a list of claims. Basically you have three options on how to respond to a claim. Yes I did it, No that never happened, Yes that happened but not how X claims it happened.
So he has basically gone for option 3. This isn't an admission of guilt of abuse. For example if you say, for arguments sake, he was annoyed at her noisy toy and broke it and she cried. He could say that he was annoyed at it and got up to move to the other room for some quiet time but accident tripped on the toy and broke it, and then consoled DD.
That's probably a bad example but you can see that he's admitting the incident happened, but that it's not happened how you said and thus isn't abuse.
So it really depends on what he's saying happened rather than if he agrees something happened.
In the coffee incident he could say DD wriggled out of his grasp awkwardly and it was an accident. That's not child abuse. (although presumably after enough incidents it becomes abuse? I don't know) The judge in court told me that abuse is specifically actions taken to purposefully harm. So accidents don't count although im sure if you have an accident every day the court will look at that badly.
Does that help at all? I'd recommend speaking to a lawyer even if you can't afford to get them to represent you in court. Spending an hour or two sitting down with you and putting you at ease, setting you on the right track and looking over your documents before you finalise them is just extremely helpful.