Question about the UK local elections this may

[LeftishBrit]

3. No

There may be some councils where LibDems and Tories may choose to go into coalition; but the Clegg-Cameron agreement does not affect local government, and many councillors of both parties probably dislike the agreement. For example, locally to me, it is obvious that the Tory leader of Oxfordshire County Council absolutely hates the LibDems, who generally return the compliment.(Not that a coalition would be likely anyway, given the Tories' solid majority here.)

Most council elections are based on FPTP, but you are correct that Supplementary Vote is generally used for directly elected mayors, and certainly for the Mayor of London. However, the national coalition agreement does not apply to London. Nor does it apply, for example, to the devolved assemblies of Scotland and Wales, which also use more proportional systems.