On Mariano's request I'm adding my comment on meta.MO as an answer here. This only concerns (part of) the first bullet point in the question.

There was an article [*Topical Bias in Generalist Mathematics Journals*](http://www.ams.org/notices/201011/rtx101101421p.pdf) by Joseph F. Grcar in the [december 2010](http://www.ams.org/notices/201011/index.html) issue of the Notices of the AMS. According to the text, the statistics are based on  854,547 entries from the 2000-2009 period of the Zentralblatt database. Unfortunately the article remains silent on exactly how the data was gathered, but it might be a starting point for your own investigations.

For the convenience of the readers I take the liberty of reproducing the statistics most relevant for the present question from that article:


<img src="https://i.sstatic.net/hIAhN.png" alt="" title="Percentage of all Mathematics Papers 2000-2009" />

For more detailed information please follow [this link](http://www.ams.org/notices/201011/rtx101101421p.pdf) or the ones provided above.