Use of OSM screenshots in an animation as part of a video

These are entirely valid questions, you aren't the only potential OSM user who has a hard time understanding the legalities. A few people in OSM (the License Working Group) are currently working on improving this situation and documenting our requirements a bit better, but that process isn't complete yet. So here's a rundown of the current situation.

• Regarding attribution placement, you can have a look at the current draft of the upcoming Attribution Guideline. Note that the document isn't official yet and might change, but it's probably still useful because it's in large parts based on current practice, and that particular section on video has been pretty uncontroversial among the community so far.
• The share-alike requirement for OSM data only applies to other map data, not works like images or video produced from that data. So you can publish your video under any terms you like, including non-open commercial terms. Unless you're improving OSM data before using it (e.g. by fixing incorrect information, in which case you'd have to share these corrections), this doesn't affect you at all.
• Now, the part where it unfortunately gets a bit tricky is that there's a share-alike requirement for OSM tiles that's separate from the one for the data. If you are making screenshots from the tiles visible by default on osm.org, these screenshots will be licensed CC BY-SA. What this means for your video isn't entirely clear – there are examples of using CC BY-SA works in a larger whole (e.g. a book) that isn't itself CC BY-SA, but I have no idea if/how that legally works out for video. If you don't want to risk it, it is possible to produce the exact same images using the same software that's also used on osm.org (or pay someone to do it for you), which would definitely not be subject to CC BY-SA. Now, of course it's rather absurd that the images on osm.org come with extra requirements, but pixel-perfect replicas produced by your own installation of the same software do not, which is why there's talk of getting rid of the requirement described in this paragraph. But as of now, that's how it is. (I'm not aware that anyone has ever faced legal repercussions for ignoring this particular nuance of OSM licensing, though.)

I hope this answer helps. Feel free to ask for clarification in comments!

The presentation of map data on the website is only one of many displays possible. The map data and the display of the map data on the main page (the tiles have) separate licenses.

There is a legal mailing list where you may be able to get clarifications, but as with all things OSM, this is volunteer run.

I am not a lawyer and can't give you legal advice, but you might find the following useful in making up your own mind.

For the underlying map data

There is a legal FAQ here which contains questions specifically about the Share-Alike aspect.

For the tiles

I know of no specific FAQ for the tiles old versions of the map data used to be CC-BY-SA 2.0 and the FAQ mentioned above links to an old FAQ about that licence here.