Until the 17th century 'often' was pronounced with the 't'. Then pronunciation without the 't' became more predominant in both American and British English. Today both pronunciations exist and are considered as standard, so you can choose how to pronounce it!

In my dialect and a lot of northern British English accents it's kind of there, but kind of elided into the F. So my pronunciation would be "of-(t)'n"

I often do it.

It's entirely your choice. Even better, it's not tied to any regional style of speech. Personally, I drop it.

You are supposed to, but the majority of people don't pronounce it -- especially kids, teenagers, or young adults. If you do pronounce the "t" you will stand out, but no one will correct you on it. It will just sound like you are speaking very properly.