Learn English – Difference between “set as” and “set at”

Virtually means "almost (in respect to degree or strength)" or "almost completely".

In your first pair, the difference is very small:

This mission is almost impossible to achieve.

This mission is virtually impossible to achieve.

Here, I think virtually is a stronger choice, so the second sentence simply means the mission is more difficult than the first. Both sentences mean basically the same thing.

Your second pair has a much bigger difference:

He was almost killed in that accident.

He was virtually killed in that accident.

Here, the first sentence can mean either:

• He was almost hurt in an accident, but he wasn't hurt at all. (For example, his car almost fell off a cliff, but it didn't fall. He got out safely.)

• He was hurt very badly in an accident. He almost died from his injuries.

On the other hand, the second sentence (with virtually) can mean only the second sense. He was hurt badly and was close to dying.

Perhaps a good rule is to imagine that the adjective modified by virtually really is true, but then take a tiny step back:

He was killed in that accident. He's dead.

He was virtually killed in that accident. He's been in the hospital for a month.

Wouldn't (or would not) is the conditional form of won't (or will not).

Don't (or do not) is the negative form of do.

Essentially, the sentence

We wouldn't say "I'm having my friend".

has the same meaning as:

If we wanted to be grammatically correct, we would not say "I'm having my friend".

In this context, the first part of the statement (the "hypothetical" half) is left out because we tend to understand the conditional phrase even without the "if" part of the sentence. Based on the context of the sentence, we infer the part that is missing.

Using "don't" instead of "wouldn't" changes the meaning of the phrase, but not greatly. For example, you could say:

We don't say the phrase "I'm having my friend" in English by itself because it is grammatically wrong.

We don't say "I'm having my friend" unless we mean "I'm having my friend over for dinner" because it doesn't make sense otherwise.

There are other sentences you could make with that phrase—these are just examples. However, the important point to notice is that it changes the meaning from being a hypothetical situation to a factual statement. Also, "would" tends to have a polite or teaching suggestion tone to it, while "don't" is less polite. "Don't" can be harsh or simply factual based on the person's tone.

(This is based on my impressions of the two from English-speaking Canada.)