1. Assuming you place some Google ads on your page – that is extremely dynamic and there is no way to get the ads to match your content – how much would you expect to earn for impressions alone? Google does track users with cookies so, they should be able to optimize ads for each user.

2. For what amount of time does an ad have to show for it to count as an impression? If it exceeds that time, does it count as two (or more) impressions?

3. If the ad is placed at the bottom of the page where it may never be visible to somebody who saw the top part and left – would that count as an impression?

4. How can you ensure that Google sends CPM ads instead of CPC ads.

Actually all your questions get answered by this statement – google ads work primarily on CPC basis and I really don’t know if you can get CPM ads. So,
a) yes, google does use cookies and can show relevant/contextual ads – provided your content is accessible to their crawler
b) per page/ad load is counted as an ad impression. If the ad appears, an ad impression is counted, even if it is a millisecond. Keeping that ad displaying for hours would not increase its impressions. The page(to be specific, the ad) needs to be refreshed/reloaded for another impression.
c) If the page with the ad loads, it will be counted an impression, irrespective of whether the user can see it or not.
d) beats me. CPM ads are very very scarce (to the extent that I believe they don’t have any) I have only seen CPC ads.