One fateful day, all of humanity was petrified by a blinding flash of light. After several millennia, high schooler Taiju awakens and finds himself lost in a world of statues. However, he's not alone! His science-loving friend Senku's been up and running for a few months and he's got a grand plan in mind, to kickstart civilization with the power of science!
There's a very brief mention that a predatory character won't assault someone when they find out they're a boy. I'm not sure if this really counts, but it's mentioned in a joking light so better safe than sorry
characters are followed without their knowledge initially in order to tell if they are carrying a weapon, in turn that person is followed to apprehend her.
Tsukasa is shown to be physically abused by adults in flashbacks, he also participated in illegal underground cagefights before becoming a pro MMA fighter
Parents appear to be deceased
A character is addicted to cigarettes and is basically never shown without them. Another character consistently makes comments/jokes about it, but they are close so it doesn't seem malicious
There is a girl who was brain dead at 6 before the petrification but she was revived. Multiple characters die, some of them being children/teens, but they are brought back to life.
if you count senku's father as a major character, yes. there is also a main character dies in a way by getting basically frozen so that his life may be saved later
They're used a couple times while performing surgery. Nothing about the needle going into the body is shown on screen but it is mentioned and the needles are shown. This happens at least twice that I can remember
If you really look into it, you could interpret it that way, but it's not portrayed as that. But for the sake of warning, a guy who is grieving his sister becomes an mma fighter and later kills people after the petrification event
characters crossdress in order to infiltrate an enemy base, and one of the characters who does it is extremely against it at first. Although I don't remember the characters themselves making any remarks, the whole scene is made as comedy
One guy fantasies for a brief moment about the possibility of two sisters marrying each other. There has also been a group of people descended from only 6 people who has survived for thousands of years, so although it is not mentioned, incest would have happened.
(1) Someone lies and says a character is drowning when they're not; (2) Three characters crash in a space capsule in the ocean but they're eventually rescued; (3) two characters sail off in a rowboat in a storm but never return — it's not shown on screen but it's assumed that they drowned.