Which adjective is better to describe 'weather' and 'climate' that they are neither cold nor hot? [closed]

Scorning the unsupported answers given in the comments (although those may be correct, as far as they go, they're not complete), I'll suggest 'moderate':

  1. Not violent or subject to extremes; mild or calm; temperate: a moderate climate.

[moderate. (n.d.) American Heritage® Dictionary of the English Language, Fifth Edition. (2011). Retrieved January 17 2016 from http://www.thefreedictionary.com/moderate .]

For your questions 1-3, then,

  1. If talking about 'moderate' weather, we're not necessarily talking about 'climate'.
  2. 'Moderate'.
  3. Yes.

Examples:

  1. The moderate weather in Washington State does not often produce violent thunderstorms or tornados.
  2. The moderate climate of the state is produced by the tempering influence of the warm North Pacific Drift. Temperature extremes are unusual as a result of that influence.

In addition to these great answers,

Clement:

Clement weather is neither too hot nor too cold. (Longman Dictionary)

It is a very clement day. (Oxford Dictionary)

Hawaii is known for its delightfully clement climate. (Merriam Webster)

The area is usually known for its clement weather. (The Free Dictionary)