Learn English – like a visit or like visiting

In my opinion, none of the above sentences are correct.

Like can be a preposition, and is used before nouns and pronouns to talk about similarity. For example:

He ran like the wind.

or

A person like you knows that..."

As, on the contrary, is a conjunction. It is used before a clause and before an expression beginning with a preposition. For example:

Nobody knows her as I do.

or

In 1939, as in 1914, everybody seemed to want war.

It is true, however, that in informal English, like is frequently used as a conjunction instead of as, so the first sentence "Do like we do." could be heard.

The third sentence is wrong because you are making a comparison and in this case as is the only one you can use. If on the contrary the concept which you want to convey is that the girl is tall and that your sister is tall too, then like is perfectly fine, but you need a comma to separate it from the first part of the sentence (that is, "She's tall, like your sister.").

Finally, you normally also use as when talking about the function or the role of something. For example:

He works as a waiter.

or

Don't use that knife as a screwdriver.

Disclaimer: The grammar explanations and most of the examples are taken from Swan's "Practical English Usage".

This is synecdoche, and it is curt and slangy, and probably derogatory. Keep in mind that mildly derogatory slang terms can be used affectionately as well. A similar example comes to mind: say you're the driver to a ski trip? You might be referred to as "the wheels." It's derogatory in the sense that that's now your purpose, flattering in the sense that your pals trust you with the role, or think you are good with it, etc.

When you use synecdoche like this, you are saying that being a suit or the wheels is the person's only relevant function.

• You could use it as a slur, e.g. "Suits aren't welcome here."
• If you meet a friend with a businessperson and say "who's the suit?" that would be mildly offensive also.
• "What's with that bar? Seems like there's a lot of suits in there." probably implies that you think suits are a type of person and probably a type you don't like.
• A software developer might say to a colleague helping her on the project "oh he's just the suit" to mean "he's not important right now, because we're talking about technical stuff."
• If you are an engineer you might introduce your partner as "the suit," which is affectionate because it is derogatory and no harm is meant. But, it is also an expedient way of saying "my partner does all the business stuff," which is ironically very important but also far removed from what "I" worry about.