Some Japanese websites have no problem addressing me as Amandaさん, but how common is this in human-produced Japanese? Under what circumstances would someone refer to someone else as Amandaさん, בועזくん, or Екатери́наちゃん instead of アマンダさん, ボアズくん, or エカテリーナちゃん?
Non-Japanese names are usually written with Japanese letters in Japanese text, but it is not rare to see them written with the original letters, too. I do not think that use of honorifics is related to whether foreign names are spelled in kana letters or in the original script.
It's used quite normally. My business emails, spam mail, post from the bank or government are all normally addressed to
David 様, or whatever exact name they happen to know me by. The same goes for more informal communication using 〜さん or other less honorable honorifics. A certain client of mine is addressing me as
DAVID SAN in emails. Non-roman, non-Japanese alphabets probably won't be used that easily though, mostly because few people can understand or write them. If you introduce yourself to people using the katakana spelling of your name, people may be more likely to use it instead of rōmaji. It always depends on the individual author though. Some will try to find out how to spell your name in kana, others may be glad for the opportunity to use rōmaji.
I can only speak to my personal experience, but my Japanese coworkers usually refer to us as [English First Name]さん (like Michael さん), even though we sometimes sign our emails in Katakana.
Perhaps it's because the Katakana isn't always exact (in fact, some names sound completely different in Katakana because the syllables don't exist in Japanese). By using the original language, they can write your name as it was meant to be written instead of a foreign adaption of your name.
Both of my language partners call me William-san all the time on the phone and in written communications in both English and Japanese.
I only use 'san' in Japanese when speaking to them, though. (English is my native language.)
Perhaps unrelated, but my Japanese teacher though told us to learn the katakana version of our names, always calls me by Joseph-さん
while taking attendance she calls everyone by [name]-さん so I was thinking the katakana version of our names is just for fun/show