I know you mentioned that you preferred iphone os, win mobile, or android... however did you consider the blackberry os? I was in the same situation as you and got the Blackberry Bold 9700 because I wanted to wait for the next gen iphone coming around summer time. I'm actually very impressed with this... As per your requirements:
- Listening to mp3s - audiobooks to be precise: no problem at all, easy to sync media and playlists
- Taking pictures and movies: decent camera quality altho still behind nexus one of course
- Writing a lot of writing using www.evernote.com
: there is an evernote app plus plenty of alternative apps for note taking... i find teh tactile keyboard allows me to type much more freely, naturally, and accurately than the touch screen (especially without those iphone's suggestions)
- Managing my daily tasks using www.rememberthemilk.com
: one of my main reasons why i went with the BB was the great free opensource app available ... bbrtm.. better than Milksync
- Writing emails: It's a Blackberry! Best email management and push email experience... great if you have multiple accounts... it requires a few extra taps on the iphone.. also, I like the centralized message inbox that gathers all messages even from certain messaging apps...
- reading books (pdf): ok.. if you don't mind teh smaller screen
- reviewing notes with anki : still looking for a free flashcard learning app... but i guess you can always use teh mobile web version
- playing multiplayer games with ur girlfriend: err.... no comment
Multi-tasking is pretty good... I didn't have any issues with lag yet.... i just don't like that you have to click the menu then close.. wish there was a shortcut key (unless if I'm mistaken).
Battery life isn't great but better than the iPhone... it is at least replaceable as is the flash memory... unlike the iphone.
Bonus: for all FARR users they have an app that does a watered down version of searching mobile sites called Beyond411... so you have quick text lookups for your (predefined) needs.
Note: I had to exchange it in for a new keyboard because it squeaked... just test it thoroughly before buying.
Although surfing isn't bad on the native browser or Opera mini it still isnt' the iPhone or Android webkit browsers... it just isn't as fun and intuitive navigation but still good enough for my purposes.
Honestly, if you can I'd wait until the next gen phones come out this summer so that it may reduce the risk of buyer's remorse