at school I learned some things which are probably (now ?) wrong:
I learned that you go “to the dentist’s” and “to the doctor’s”. Is this wrong and you have to say “to go to the dentist” or “to the doctor”, respectively ?
My second question is:
Are “to characterize” and “to characterise” both fine in British English and “to characterize” is correct in American English ?
Both forms are acceptable. The spelling of these words with ‘s’ or ‘z’ technically depends on whether the word has its origin in French (s) or Greek (z). That said, both forms are used and acceptable.