1. Yes, I think that is the idea. But the AI will never give away more than 25% of a resource, at least that is my experience. If they have less than 4 of a certain resource you are stuck ... (or have to resort to war).

2. Sometimes I get resources by anomalies, but so far only the commons ones. I don't know whether one can also acquire special resources that way.

3. I don't know what exactly is intended. I play only the largest maps and there you eventually find everything, but I don't know whether there is a galaxy generation logic that guarantees that every resource exists at least once for every map size.

1.  It seems to be that everything will be there in one galaxy.  There are sightings of galaxies with a missing resource.  I haven't seen that.  Size of map may affect things.  Any scarcity of resources is definitely intended as progress choke points.  This is intended to drive conquest and trading.

2. Not that I know of, no.

3.  It is intended to be rare enough to fight over or negotiate for.  If it is completely missing, it cannot perform that function.  I expect there is some weighting going on.  I do not expect that complete lack of any one resource is not directly intended, but may be an accepted consequence as smaller maps and weighting algorithms impact each other's operation.  However, on a medium map, That is much less likely.

My prediction is that you will not likely see a complete lack, but you may see one resource source per galaxy with the settings you play.  With smaller maps, there may not be enough planets to support the planet sourced resources unless the planet generator is set to force the issue.  Let us know what you find!

The resource missions mod is wonderful and should be part of the base game. The ai even makes good use of it.

I've had several galaxies that were completely missing some resource or another. Usually it has to do lack of black holes, asteroids, or nebulae. You probably won't see those scenarios unless you set the map generator to rare or random for those elements. My current game in a large galaxy has absolutely no elerium. Zilch. My last game had no durantium which meant you could not upgrade building or star base modules at all.

Yesterday I figured out that Amor Spice, apart from upgrading Entertainment Centers, can also be used for a "promote scientist" action that finishes your current research immediately, which is immensely powerful (e.g. I used it to finish a 24 turn research in 1 turn, for just 10 Promethion and 1 Amor Spice).

This is confusing enough on it's own - I mean, unless you had an excessive supply of Amor Spice or shortage or Promethion, why should you ever use it to upgrade an Entertainment Center instead of rushing your research? - but it also means that getting a grasp of how resources work is more difficult than I thought. I guess for each special resource there is a very powerful way to use it somewhere, and you have to find all of them to be able to effectively use what you have.

The Amor Spice promotion doesn't even kill the researcher, you just have to pay 10 Promethion and 1 Amor Spice. The promotion that kills the researcher requires Malevolent ideology and has different costs.