How much radiation is safe?

I threw your questions at ChatGPT, and got some interesting responses.
First, it said any reading under 1 Sv was generally safe. However, it also pointed out that when the Fukushima incident occurred, the Japanese government was recommending anyone in an area experiencing 1 μSv/h should either evacuate or seek adequate shelter.

The Sv dosage to decide to leave a shelter would be the same as the one to seek shelter. If you have a means to protect from breathing in radioactive particles, and can adequately decontaminate upon returning. short runs to leave the shelter can be somewhat safe. Long exposure will depend on the local Sv reading. Don't dally.
This is based on information available in a reference manual I keep titled The U.S. Armed Forces Nuclear, Biological and Chemical Survival Manual by Dick Couch, retired Captain, USNR.

When to take iodine would depend on the type of nuclear incident. If from a fission bomb, radioactive iodine is highly likely to be produced. From a fusion reaction, not as likely. Children are more susceptible to the effects of radioactive iodine, and should be given proper dosing first. Then pregnant and breastfeeding mothers should be next on the priority list, as they are nurturing a susceptible baby. Finally, adults are less affected but the situation could dictate that they be administered a dose too. It's hard to know for sure when without knowing the variables in play. Unless you know it should be given, there's some risk with taking it as a precautionary measure "just in case". Some folks are allergic. Others can have gastro distress. Self-medicating isn't recommended unless you've had this chat with your doctor ahead of time and received proper instructions.

If you're keen on reading, the manual I mentioned had a list of online references for more research.
One of particular note was: WMD Army Field Manuals
Enjoy.