No, you don't need anything else - this is adaptor with power converter build in - plug is European type except UK. If you are not planning to go to UK this is enough. In case if you will be in UK you have to buy just adaptor. If you are going to Europe and will carry more equipment as laptop, iPad or mobile phone then I would suggest to you just buy on the plane universal multiadaptor - you can use all your devices' chargers everywhere around the world (of course you have to check if your chargers are suitable for 230-240 VAC but from my experience, Kindle, iPhone, iPad, laptops and mobile phone charges are typicaly for 100-240VAC 50/60Hz - take a look at adaptor aand you will find this information). Delta, KLM, Air france or BA for sure have multiadaptors in plane onboard shop if not you can find them also at the airports in many shops with electronics. Avarage price is around 20-30 USD but then you won't have any more doubts wherever you will go.
Were you able to charge it from the wall in Israel? It looks to me that the only thing to do is find a plug with the prongs like they plug in Israel (cheap and easy to find there in any hardware store), and the AC adaptor that comes with the Kindle should do the trick. It is a 100-240 , 50/60 cycles adaptor, afterall. If somebody has an answer, please write.
Yes, the Amazon power adaptor is good for Paperwhite as well as other Kindles however it is expensive (20 dollars). Any USB power supply 5V will do including if you already have a Kindle power supply. Paperwhite is truly 5 star.
The EU adaptor probably won't fit the Japanese/Chinese wall sockets. What you would need is the International Wall Home AC Charger for Amazon Kindle / DX / ... by Gomadic or the Kindle PowerFast International Charging Kit by Amazon. Those include the Japanese/Chinese type plugs.