"I was obviously on the nod and very exhausted, falling asleep, and the ice cream then spilled all over my leg and then she took that ... and showed me the next day and said "Look at what you've become ... look at you, it's pathetic".
The two incidents are among 14 allegations of violence towards Heard The Sun's lawyers have submitted, all of which the actor denies.
"I could hear the ruckus inside", Connolly said.
Roberts said she had seen Heard "screaming and berating" Depp as he shouted at her to "go away", and claimed to have seen a "red, swelling gash" on his nose.
He said the actor "made a playful attempt to tap her on the bottom", adding that he did not believe that Mr Depp made contact with her.
"She also alleged that general socialisation or moments to discuss "island issues" stopped as Ms Heard would "randomly show up" and that she would "'wiggle' her way" into discussions.
The actor is suing NGN and Mr Wootton over the publication of an article on April 27 2018 with the headline: "Gone Potty: How can JK Rowling be 'genuinely happy" casting wife beater Johnny Depp in the new Fantastic Beasts film?' The barrister asked: "So, if a fight had taken place at 3.30 in the morning, do you think you would necessarily have known about it?"
"Ms Heard took great offence at what was clearly a harmless gesture and increased her abuse of Mr Depp in an extremely unpleasant manner", he said.
Depp says Heard "severed" his finger with a broken vodka bottle.
Depp rejected all the allegations that he attacked his wife and said Heard was lying, making up a choreographed hoax as part of an "insurance policy" dossier, and that she had attacked him.
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Mr Depp said: "I was in the early stage of learning from my recently acquired new business manager that the former business managers had (taken) quite a lot of my money".
Mr Depp replied: "Definitely not".
In the text, Mr Heard also wrote: "But I still love you like a father or brother".
Ms Roberts alleged that she saw Ms Heard "lunge violently at Johnny, pull his hair, and commit other aggressive physical acts against him".
As he began giving his fifth day of evidence in his libel action against The Sun newspaper, Mr Depp denied an alleged incident of domestic violence against his ex-wife Amber Heard in March 2015, saying he would have been unable to attack her because he was wearing a cast with "a little dinosaur" on it at the time.
A concierge who worked in the building where Mr Depp and Ms Heard lived told the court she had seen CCTV which made her doubt one of the actress's assault claims.
Judge Andrew Nicol was told Mr Depp had headbutted, slapped, kicked, threatened and thrown bottles at Ms Heard during heated arguments.
"He continued to stand there yelling at her to stop and leave him alone", she said. The actor is also suing his ex-wife in a separate case in the United States for allegedly presenting him as an abuser in a Washington Post article.
Connolly recalled Depp telling him that Heard had put a cigarette out on his face, and he saw a mark on the star, but no injuries on the actress.
Witnesses including Mr Depp's former partners Vanessa Paradis and Winona Ryder are expected to give evidence via video link, and the hearing is expected to last for three weeks.