Are American books translated into English UK?

It depends largely on the policy of the individual publisher, but also on the cost of revision and new composition versus the degree of tolerance of the target readership. US publishers, having a larger readership (and one less familiar with or tolerant of, the peculiarities of the other, smaller, society), are much more likely to Americanise spelling, terminology, etc., than their British equivalents are to Anglicize imports. A frequent exception is books dealing with technology (e.g. the domestic electric supply) that differs on the two sides of the Atlantic. In the past when authors negotiated separate contracts for the North American and British Commonwealth rights, different editions were, naturally, the rule.

Titles (as a book’s most important selling point) are most likely to be changed. Jonathan Cape turned Hemingway’s “The Sun Also Rises” into “Fiesta,” presumably as making the book’s Spanish setting more obvious. “Harry Potter and the Philosopher’s Stone” was deemed unintelligible for its North American readers and had to be changed.

Before World War I when Portugal had a much larger book industry than Brazil, the few Brazilian books it deigned to publish underwent adaptation far more radical than just spelling. Nowadays, with the position totally reversed, few modern Portuguese authors, other than José Samargo, are ever even considered for publication in Brazil.

Extensively illustrated books are least likely to be changed (too expensive).

No, they're not. Written English is pretty much the same. Although there are slight differences, most people can understand the differences between American and British English. It would be a ridiculous waste of time to go through entire books just to change a few words.

No. The difference is of spelling rather than vocabulary. Also books are heavy so generally a book for the UK will be printed in the uk with british spelling and the same book will be printed in the USA with US spelling,.

Few Brits have difficulty deciphering the regional dialects we have in the US. A few terms, like "antegogling" may temporarily throw them (they throw some of our fellow Americans, too) but we really don't have that many such words or phrases.

Antegogling means to walk a crooked path - to wander from over here to over there.

Very rarely, but UK books seem to be often "translated" into US English.

No, the US thinks they speak perfect English. I'm in Joao Pessoa, and the US Americans argue with me, A Brit, that they speak proper English.

Some books might be, but I think I remember reading a book where they mentioned 'egg plants' here they are known as aubergines.

I don't think so. It would be pretty pointless seeing as the differences are generally pretty small.