Not really a typical child abandonment scenario, but Noodle was only about 15-16 when she disappeared after El Manana, though the details of this event are murky, they could be interpreted as the band/Murdoc unwillingly abandoning her
All of them are smokers, though Murdoc and 2D are more prominently depicted smoking.
Murdoc is also an alcoholic and has used various drugs, and 2D is/was addicted to pills, notably in the first three phases.
Though never shown, Murdoc has been sexually assaulted multiple times in his past. He first got sa'd by a dinner waitress when he was just 9 years old, as stated in the Rise of the Ogre book, and he mentions it in one of the pirate radio sessions, in which he is under distress.
He has also been sa'd while he was in jail in Mexico, though this has been treated as a joke, sadly.
The phase two ident which is set in that jail also ends with the implication that he will get non-consensually fingered.
In the Clint Eastwood music video, a zombie gorilla hand emerges from the ground under a character, grabs him by the crotch and forcibly pulls him to the ground. (No, I am not making this up.)
At the start of Phase 3, before the main events of the Up On Melancholy Hill music video, there is an ident of Russel jumping off the docks into the sea. It’s not completely clear if it’s more of a suicide or a quest/plan to him, but he leaves a suicide note behind, which is on the Gorillaz wikia. There is some unreality in his writing and there are some blood smears on it so please be warned.
We do not see him suffer after he survives - the next time we see him he has turned into a giant. He’d survived his attempt because he’d inadvertently ingested a lot of polluted waste in the water and he started transforming large enough to walk on the sea floor.
There are many instances (especially in music videos for Tranz, Sleeping Powder, and Saturnz Barz) where reality is warped. A common theme in Gorillaz lore is also that some things seem plausible but couldn't actually happen.
2D notably has an anxiety attack as a whale comes towards him in the water in the Rhinestone Eyes storyboard. In phases 1-3, he is frequently shown being afraid or panicking.
In one of the phase 3 interviews, 2D rants about his situation trapped on the plastic beach and shouts ‘It’s making him want to die’ but Murdoc cuts him off and this isn’t dwelled on.
Not directly. In a short cartoon segment Murdoc dresses as a N**i for Halloween and does not seem to notice any problem with it. Russel promptly tears him a new one.
Sad to say but Noodle’s representation is a bit awkward in the early phases (mainly being drawn with slanty eyes) although fortunately is toned down much later
In On Melancholy Hill Noodle manages to shoot down a plane and it falls in to the sea. This occurs at around 0:45-0:52, and it is slightly graphic, because she manages to shoot the pilot so we can see a blood spray in the cockpit for a split second.
In the Rhinestone Eyes storyboard video we see a whale get thrown onto a plane mid-air causing it to break apart and crash into the sea. The pilot is implied to have died, but the whale seems to be relatively unscathed.
In a phase 2 game, which I am not sure if its available/playable anymore-but there are videos of it on youtube, you have to transplant all of Murdoc's organs and spine to 2D's body and vice-versa. It has some minor blood, but the organs are drawn in high detail. Murdocs organs are also very damaged and are much less healty than 2Ds, and the procedure is non-consentual on 2D's end.