We would say crime or broke the law for all of those. Of course, there are levels of seriousness. Offenses (driving without a license), misdemeanors (sneaking into a plant territory), felonies (murder), and treason are levels I'm aware of. They are all crimes. I have never heard of an administrative offense, but if murder or stealing isn't an administrative offense, then in English (as least American English), you might call it an offense or misdemeanor.

Phil, Michael, thank you!!! Michael, in Russian we use words "crime", "criminal" only for those offences, which are in our Criminal Code. These are serious offences against society and state. The criminal records are stored and matter for you as a person. Minor offences against society and state are in the Administrative Code. They are forgiven after one year since being committed, without respect of being sentenced or not. The Civil Code contains acts against interests of other person (group). For example, your neighbors could demand reimbursment for your mischiefing for three years before since they noticed that. That's why I asked the question

In English law and the law of other common law jurisdictions (as far as I know), "offences" are only criminal. Technically, we use the word "wrongs" (or "torts") for breaches of civil laws. We don't have a third category of administrative offences. Most administrative matters are civil.

“Crime” is a general word in English referring to both misdemeanors and felonies. What you’re describing would probably be “misdemeanors” in the USA (depending on the jurisdiction, the value of the train fare, etc.). A more serious crime would be a “felony” (grand theft, murder, etc.). A less serious matter, like a speeding ticket, is an “infraction”. A parking ticket is even less serious, although I believe it would still be an infraction.