Could you explain the differences of these expressions for me?

a little/ a bit/ a little bit/ slightly

One more question;
In formal speeches and letters, should I avoid putting the expressions with "bit" in sentences?
"Little" and "bit" can be considered synonyms, but the latter is informal and mainly used when one speaks. In formal speeches it should be avoided. "A little bit" is an informal way of saying "little" (emphatically?):

A: Would you like more wine?
B: Just a little bit, thanks.

"Slightly" is and adverb meaning "small in measure or degree". It's formal or neutral:

Turn up the radio slightly, please.
They are slightly different.

You can use "little" as well:

Turn up the radio a little, please. I love that song!

Now, there's a slight difference in use between "little" and "a little". "Little" implies a negative sense while "a little" conveys a positive one. Examples:

This political party actually has little power.
Hey, don't buy more bread. I have a little and it'll be enough for dinner.
Students: Are you brave enough to let our tutors analyse your pronunciation?
Thank you very much for explanation Emotion: smile

Could you please check the following sentences for me?
I'm not sure where to put them in the sentences correctly.

The room was slightly cold.
It was a slightly cold room.

How about these ones?

The room was a little cold.
I had an examination in a little cold room.
I had an examination in a slightly cold room.

They are all okay. Emotion: smile
Sorry, if I sounded a bit rude, but I´d like to know if it is possible for to help me to find some information.
Students: We have free audio pronunciation exercises.

When can I use the phrase "a little"?