What should I absolutely not do when visiting your country?
Don't tip anyone. No one. NO ONE.Tipping is just not part of the culture. Don't even leave the small change. People will come running after you with it. Seriously.
Don't go into people's homes with your shoes on. You may run into this at certain temples and shrines, restaurants or traditional inns too. If you see other people taking their shoes off, do the same.
Do not enter a bath tub without washing yourself outside the tub first, especially at onsen springs, or at public baths (sento).
Stay on the correct side on escalators. In The Tokyo you stand on the left. In Osaka you stand on the right. Follow what other people are doing.
Kissing in a public place. In some jurisdictions this can get you into jail under "public obscenity" (a lot of our laws are stuck in the Victorian era). Although the law enforcement cuts some slack if the couple is married, if the couple is unmarried things can get really messy.
Shorts/skirts in a place of worship. Dresses that show anything above the ankle is generally frowned upon in most places of worship and in someplaces officially banned. This applies to both sexes.
As far as I'm concerned, there's only one "absolutely not" rule for Germany:
Don't do the Nazi salute. Not even in jest. It's a crime and every year there are tourists arrested for it. Also don't carry any Nazi symbols on you.
Don't give even number of flowers as a gift. That's for dead folks. Proper bouquet will have 1/3/5/7/... flowers.
Don't criticize Soviet Union when talking with people over 40. They grew up at those times and might be nostalgic. Even if they enjoy modern life they might not like hearing foreigners talking about it.
While in Singapore...
don't feed birds. They'll fine you.
don't spit. They'll fine you.
don't urinate in public. They'll fine you.
don't bring durians into enclosed areas. They'll fine you.
don't smoke in public. They'll fine you.
don't bring pets into public. They'll fine you.
don't eat or drink on public transport. They'll fine you.
don't litter. They'll fine you.
don't bring flammable goods. They'll fine you.
don't take drugs. They'll fine you.
don't walk around naked in public. They'll review or even take away your prestigious scholarship. Then they'll fine you.
don't bring more than 15g of heroin here. They'll kill you. (Capital punishment in Singapore)