If it's the criminal record you want to focus on, then specifically in the UK, offences that are placed on your criminal record are referred to as "recordable offences": https://en.wikipedia.org/wiki/Recordable_offence
All other offences therefore are "non-recordable offences". I'm not aware of a single word with that specific meaning.
Note also that we don't definitively say (in the UK) that non-recordable offences "are not crimes". They are crimes, they just aren't on your criminal record. In that sense, the criminal record could be seen as containing edited highlights rather than your full criminal activity. There are certain contexts (such as a military security clearance) where you might be required to reveal convictions that are not recordable, and even matters dealt with by a fixed penalty notice rather than a court.
If it's "non-crime" you want to focus on, rather than criminal record, then things are a bit more tricky. UK legislation talks about "offences", not "crimes", but generally any offence under criminal law can be called a crime. Once found guilty it's a "conviction", again this refers to any degree of wrong-doing that made it to court.
I don't think there's any specific word meaning "naughty things that the law deals with by making a fine or fee payable, but that are not criminal offences". In fact there's some ambiguity in the language, when people talk about "having committed a crime" it's not always clear what they include and what they don't.
Looking at your examples:
Some parking violations are offences (parking on a motorway, for example). Sometimes it's merely an action for which the local authority is entitled to charge a fine/fee.
Not wearing a seat belt breaches the Motor vehicles (wearing of seatbelts) regulations 1993, which were authorised under the Road Traffic Act 1988. I haven't investigated the details enough to discover whether a breach of those regulations is an offence or not.
For a pedestrian, crossing the street on a red light is legal (unless you recklessly endanger traffic, but then the offence is not crossing the street, it's endangering traffic).
Drinking alcohol in public is regulated by the Criminal Justice and Police Act 2001. In certain areas you can be ordered by a police officer to stop drinking, and then refusing is an offence.
Failing to complete an electoral registration is not an offence (I think). Evading council tax is, so in practice you have to register your place of residence if you're eligible. The address on your driving license is required to be correct, although this is often flouted and I don't know whether it's an offence or not.
Leaving aside the tax evasion, I don't think any of those that are offences is recordable, and people would generally object to being called "a criminal" based on having committed one of them.
All in all, I think the best phrases for what you're talking about are "non-recordable offence" or "minor offence". But if you want to include things that aren't offences at all then it's more difficult to find a term and even ambiguous what it should cover.