Is taking a year or so off between master's and PhD to self-study or do independent research a common practice in Europe? So from my previous questions and from what I heard, I found out (iirc) that people who apply for a PhD in the US make a personal statement or statement of purpose while those in the UK, and I infer most of Europe, make a PhD proposal.

From what I understand, this involves reading several textbooks or journals (IMHO, there's a lot more reading to be done if one is changing fields).

So, is that what students intending to study in Europe commonly do? How long does this take? I mean, should much of one's PhD proposal research have been done in masteral studies?
While your background (education, skills, experience) should fit for a PhD vacancy, it is generally not necessary to write your own PhD proposal.

Many (most) universities in Europe have a section on their website that lists open PhD vacancies (either on the top level of the university website, or at the individual institutes).
It is best to find a vacancy that fits with your interests and background, and simply apply for it (by sending an application letter + CV).

There are some websites that list open PhD vacancies for multiple universities, e.g. 


for the Netherlands: https://www.academictransfer.com/?language=en
internationally: http://www.careeredu.eu/


You can have a look there whether you find any position that suits you.