Take the Mickey, take the piss, and making fun of someone all mean the same thing.
Take the Mickey can have two different meanings depending on the context.
One meaning is to make jokes or make fun of someone.
Another meaning is to take liberties or take advantage of someone.
Take the Mickey is an abbreviation of taking the Mickey bliss, which is cockney rhyming slang for take the piss.
To take the piss is the more rude version of take the Mickey.
Are they taking the Mickey? means are they being sit?
It's all right, I'm just taking the Mickey means I'm just making fun of you.
An announcement on the message board that says the train's been delayed three hours can be an example of taking the Mickey.
Finally, here is the third part of this series about English slang words and expressions that most British people know, but which will probably confuse almost everyone else! I started this series in 2019. It's only taken me nearly 4 years to get round to finishing it. Learn loads of slang and culture, plus a bit of British history too.