For online I don't know. I only know latin->hebrew, by making an HTML page!
Locally one can go both ways in a good text editor quite easily.
For locally, dump notepad for this task, as while it supports UTF-8 and unicode characters including hebrew ones, it doesn't encode in Windows-1255(Hebrew) so when you try to save unicode as "ascii" it's not using windows 1255(hebrew). just 1252 or iso 8859-1 and it would not do it properly as the hebrew characters don't exist in 1252.
The funny characters-latin ones, you see is 1255(Hebrew) misread as 1252 - you can do that, but you can't save hebrew as 1252 'cos notepad wouldn't know or doesn't calculate which latin characters to use. It just says you'll lose some characters and if you try to save them it won't and when you read them after it hasn't saved correctly, you'll get question marks or squares. So forget notepad for saving hebrew characters
Use a text editor that supports Windows-1255(hebrew ascii). It works in editpad pro(not free). But notepad++ or babelpad probably do it just as easily too (though none of those programs are so good at the moment for pasting from them into ms word. epp you copy hebrew it pastes latin characters, notepad++ and babelpad you paste into word and don't get the "keep source formatting" option) but you can put the hebrew into an html page(like the utf-8 one in the question), and then copy it from chrome into ms word.
open editpad pro, click convert..text encoding.. windows 1255
copy/paste the hebrew characters from notepad into editpad pro.
save the file.
And you can go both ways.
úåøä ----convert to windows 1255 (should also open as 1255) get the hebrew. And convert back to 1252 (should also open as 1252) (western european)