Learn English – What does “talk to the hand” mean

This is in reference to a 'blue movie', a euphemistic term for a pornographic film.

It has since been toned down somewhat and phrases like a bit of blue can be used to say that something is 'adult' in nature. Often this includes dealing with sexual material but doesn't necessarily mean visually pornographic; a comedian who tells jokes with a sexual theme could be called 'a bit blue'.

going a bit blue then would mean that the programme/character in question is normally 'clean' but has begun to include more adult themes.

It would appear that the term has been used thus since the early 1800s, originating in Scotland, though a clear connection between the colour and the connotation has not been settled on.

N.B.: Bolton comedian Peter Kay is famous in England and well known for his family friendly stand up material. In his shows he will occasionally tell a joke with some sort of subtle sexual reference or other 'adult' theme and then follow the joke by saying 'a bit of blue for the dads there'.

It's a sarcastic response.

Taken literally the sentence would mean the speaker isn't already familiar with the situation and wants more information. However it is rarely (these days never) meant literally, and is used sarcastically to mean the opposite. I.e. That the speaker is already familiar with the situation. Its meaning is similar to the expression, "You don't say?", where the speaker is acting like they don't already know, when in fact they do.

The difference between these two expressions however is that, "Tell me about it", has taken on a sympathetic tone over the years, indicating shared misery, whereas, "You don't say?", is an insult where you don't actually care what the person has to say.

There's little in the words themselves to indicate that difference. That difference is simply the connotations those expressions have taken on over time. Tone of voice is pretty critical here, because the difference between a sympathetic statement and an insulting one is simply a different inflection while saying the exact same words.