How does the location element of a BIC work?

Question

A BIC (Business Identifier Code) consists of

• a four-character bank code;
• a two-character country code (ISO 3166-1 alpha-2);
• a two-character location code;
• an optional three-character branch code, with XXX reserved for the head office.

My questions are,

1. Who defines the location code? Who decides that 2L is London?
2. If you leave off the optional branch code, do different branches of the same bank still have different BICs (because of the location code), or do they all use the location code of their head office?
3. Do banks actually use the optional branch code and a BIC for each branch in practice? None here in Ireland seem to. As far as I can tell, the BIC for Bank of Ireland is always BOFIIE2D. I'm going to guess that 2D is Dublin, presumably the location of the head office.
4. Is the bank code always alphabetic, or can it contain digits?