Things have probably been answered but here's my take on it.
1) How regular is the weather, I've observed a pattern of east to west wind in Edinburgh. Is this likely to be the case for a long time or is it just coincidence.
The pattern is actually west to east. There's a fairly predominant west wind blows through the central belt meaning predominantly weather is blown over from the west. ie if its wet in Glasgow in the morning, it'll probably be wet in Falkirk in the afternoon and wet in Edinburgh at night. However the rain can sometimes 'wear out' before it gets here. A look at a weater radar usually confirms thi but be prepared its occaisionaly not the case, usually when I cycle West and expect to be blown home.
2) Looking at the forecast for tomorrow, I'm seeing a mean wind speed of 12mph with gusts as high as 35mph. My current average cycling speed is in the region of 14mph. 14mph into a 12mph headwind should see me progressing at 2 miles per hour? Somehow I don't think that's the case. How does (head)wind speed impact on cycling speed? I'm guessing that I'll cycle harder to compensate - how would I go about measuring that?
When there's a head wind you still get some where just not as fast. Individual air particles are travelling, say 12mph but because air is a gas some of the particles go around you so it depends how much of the particles you have to stop/ resist. Basically if you normally cycle 15mph without wind you can expect for the same effort into a head wind to be slown dow by around 1-2mph.
3) Assuming it is just raining, no wind, what kind of impact does that have on my cycling. I feel like I slow down, owing to road conditions, so I can't really tell if rain makes cycling easier or harder.
Depending on the level sometimes wet surfaces can be slightly easier as there is less rolling resistance (the water acts like a lubricant). When it gets too heavy though it starts to weigh you down and the rolling resistance actually increase. Its normal though to be more cautious in the wet, so generally it slows you down.
4) Thunder and lightening. Very very frightening. Namely the lightening, is it safe to be out in such weather. How does being on a bicycle adjust one's chances of being stuck by lightening?
Thunder and lightening happens so rarely here I wouldn't worry about it. Even if it does occur the chances of actually being struck on a moving object is limited. How many cars/ buses/ lorries do you hear about being struck in the East of Scotland.
I'm not too sure what the cold does to my cycling - I'd guess there might be some loss of efficiency because my body has to work harder to keep me warm, but to be honest I haven't really noticed anything. Then again I'm not particularly focused on training; I cycle mostly for transport/recreation. My questions are more of an intelectual pursuit...
Cold depending on its level doesn't have too much impact on the bike but it does on you (the engine) and again if its too eaxtreme (too cold) there's a risk of ice which you have to be cautious of too so this slows you down or rain turns to snow and slows both you and the bike down. The good thin when its frosty you don't have to get up extra early to scrape you windscreen etc.