Does placement matter on the map? Should I place it between the extractors or closer to my factory groups?
Nope, placement doesn't matter 
Is it really worth the return in shorter games or is this a longer term strategy?
Probably not. Mileage varies, but most agree that it's easier and cheaper to build trade ports and use the credits to buy the resources in smaller games. In large games I've used refineries, but you also tend to have enough basic income just from the number of planets you own that you don't need the extra from refineries in order to keep up with research/production. So I personally play it by ear, so to speak. I play mostly Random maps, so resources can get pretty lopsided sometimes. More in the next paragraph
Does this collect resources from other planets or only the planet that it is placed on? In other words, should I place one on every planet or stagger them? As log slots are at a premium, I typically place only place them on planets where I have more slots available, but I'm thinking that I should be placing them on asteroids... Not sure about that though...
Refineries have a range of 1 jump. So if you build a refinery at a planet, it will also serve all planets one jump away. Each colonized planet can support 3 refineries, neutral mines can support 4. This makes refineries useful in that if you have a really nice intertwined cluster of planets, the 3 refineries max out all of them. And this is my most common use of refineries. If I see that I have a very nice group of planets (usually 4+) all linked, I'll drop the 3 refineries because it will benefit all 4 planets. Otherwise, I don't really bother.
Also note that the Advent don't have a separate refinery structure, their trade port can change to serve as a refinery but without the 1-jump range, it will only work in that grav well. On the flip side, it will also give a bigger boost.
