Is there a naming convention for MySQL?

MySQL has a short description of their more or less strict rules:

https://dev.mysql.com/doc/internals/en/coding-style.html

Most common codingstyle for MySQL by Simon Holywell:

http://www.sqlstyle.guide/

See also this question: Are there any published coding style guidelines for SQL?

Thankfully, PHP developers aren't "Camel case bigots" like some development communities I know.

Your conventions sound fine.

Just so long as they're a) simple, and b) consistent - I don't see any problems :)

PS: Personally, I think 5) is overkill...

Consistency is the key to any naming standard. As long as it's logical and consistent, you're 99% there.

The standard itself is very much personal preference - so if you like your standard, then run with it.

To answer your question outright - no, MySQL doesn't have a preferred naming convention/standard, so rolling your own is fine (and yours seems logical).

I would say that first and foremost: be consistent.

I reckon you are almost there with the conventions that you have outlined in your question. A couple of comments though:

Points 1 and 2 are good I reckon.

Point 3 - sadly this is not always possible. Think about how you would cope with a single table foo_bar that has columns foo_id and another_foo_id both of which reference the foo table foo_id column. You might want to consider how to deal with this. This is a bit of a corner case though!

Point 4 - Similar to Point 3. You may want to introduce a number at the end of the foreign key name to cater for having more than one referencing column.

Point 5 - I would avoid this. It provides you with little and will become a headache when you want to add or remove columns from a table at a later date.

Some other points are:

Index Naming Conventions

You may wish to introduce a naming convention for indexes - this will be a great help for any database metadata work that you might want to carry out. For example you might just want to call an index foo_bar_idx1 or foo_idx1 - totally up to you but worth considering.

Singular vs Plural Column Names

It might be a good idea to address the thorny issue of plural vs single in your column names as well as your table name(s). This subject often causes big debates in the DB community. I would stick with singular forms for both table names and columns. There. I've said it.

The main thing here is of course consistency!