The best way I have been able to translate 「だけ」 has been to refer to limits.
「一人」 means "one person", and you'd probably be best leaving at that.
I think I have heard some people using 「一人で」 in plural, in the sense that the English "alone" can be used in plural, (clarification) thus
We did this alone.
can mean "We did this by ourselves." (It can also mean "We did this one thing." That's not really current usage, however.)
(end clarification) But I'm not sure I heard it right, and I'm not sure that the people I heard weren't using it in a non-standard sense.
When there are just two, all alone, you can use the expression 「二人」 or 「二人きり」。
I checked with both of my kids (college senior and high school senior) and they agree that 「一人で」 is not used in the plural sense. See my later comments on the "individually" meaning.
"Of course" and "eventually" can be interpreted to apply to a whole English sentence, but you really shouldn't do that. Apply to the verb when in doubt, and move it there when you need to be exact. Using your examples,
I can, of course, do this.
The machine eventually crashed.
Now, 「だけ」 does have some uses that may sound odd, but don't go looking too far away. In other words, if you think it's modifying the whole sentence, you're misreading it.
(end further afterthought)
Trying to interpret your four sentences,
This almost sounds to me like you might have been trying to say
or, "This was something that my friends and I just had to do." You probably did not mean that. Also, consider, 「やるしかなかった」。
Instead, you might have said
(something we had to do ourselves), or
(something we had to do by ourselves)
Your second sentence,
comes out as
Speaking only of my friends and me, we did this.
I think you wanted to use 「で」 instead of 「は」。
But I'm also thinking I have heard
Let's see what our Japanese friends who hang out around here have to say about that.
Ouch. Did you mean past of 「です」 or past of 「する」？
「やる」 is not a perfect replacement for 「する」、 but it comes in handy in places like this. (And it's a bit preferred over plain 「する」 in some dialects.)
Unless I misunderstand my Japanese, 「でした」 in (2a) will be read as the past tense of 「です」、 so it will be read,
In this, I was alone.
However, given what that means, it can and is used as a substitute for
so it doesn't seem like a big deal, but misunderstanding what is happening there can trip you up.
You really want to use 「しました」 or 「やった」 when saying it this way.
But you really don't want to use 「一人」 here.
(end further afterthought)
And you want to consider the "individual" meaning, as well. 「私たち一人一人」 is "we, individually". So, even if the plural sense has become accepted as it has in the English word "alone",
would more likely be read "each, individually" than "only us".
But try this on for size:
My friends and I were united in this.
And this one:
This was something I and a friend did.
Okay, if you and some friends and some others did "this", you can use 「や」 and say,
The limit is actually implicit in 「と」。 In other words,
is already read as an exclusive "and", so you only use 「だけ」 to emphasize the exclusion: