What you consider FooBuilder and Foo is actually part of a well-established Builder pattern. What you started with is also a well-known design pattern, called Prototype.

Overall, nothing you wrote sounds bad. They are well-known alternatives and books (most notably "Design Patterns", aka GoF) have been written describing them.

Each pattern obviously has its own advantages and drawbacks and only you can decide which one is better for your specific situation. For example, I would typically use builders when there's a lot of different ways of initializing Foo. For example, right now I'm working on a query builder class and many clients use it differently to build query objects. Different clients want different fields to be returned, some clients want only last 10 rows, some want sorting while others don't. Builder is perfect as it can look something like this:

qb = QueryBuilder()
query = qb.fields("name", "address")
          .sort("zip", "asc")
          .limit(10)
          .build()

So multiple setters, each returning instance of the builder itself so you can daisy-chain basically serve as a very flexible constructor. Making one class a friend of another class has it's time and a place and potentially this could be one of those places.

Alternatively, you could define Foo as having one constructor that takes a rather complex set of params, or potentially you could define another class FooData, that FooBuilder could initialize and pass into Foo creation. Then again, maybe Foo and FooBuilder being friends in this case isn't such a bad thing. Just keep in mind that when one class is a friend of another one, you are expanding encapsulation boundary, which could be just as bad as putting more and more code all within one class (i.e. more code knows about internals)

At the end of the day, you could be thinking and considering all these different options and it will all boil down to 60/40. If there's no clear winner, you can always let a coin pick the winner and just go with it. Most likely either one of the design choices would work just fine and by going through the motions and seeing your code in action you will learn valuable lesson for future. Sometimes when I have design decisions and can't decide between A and B, I could end up picking B and then if I ever come across a similar situation I would intentionally pick the other choice. The work in either case gets done and I get the software to do what I want, but you get a ton of benefit of actually seeing your decisions in action and being able to compare the two working approaches, rather than just discussing and thinking about them.

What you consider FooBuilder and Foo is actually part of a well-established Builder pattern. The other approach you mention with creating a Foo instance based on an existing instance is called a Prototype pattern. Both of these are well-known object creation alternatives and several books (most notably "Design Patterns", aka GoF) have been written describing them. (not sure I'm clear on your second mutable example, so comparing #1 to #3 here)

Each pattern obviously has its own advantages and drawbacks and only you can decide which one is better for your specific situation. For example, I would typically use builders when there's a lot of different ways of initializing Foo. For example, right now I'm working on a query builder class and many clients use it differently to build query objects. Different clients want different fields to be returned, some clients want only last 10 rows, some want sorting while others don't. Builder is perfect as it can look something like this:

qb = QueryBuilder()
query = qb.fields("name", "address")
          .sort("zip", "asc")
          .limit(10)
          .build()

So multiple setters, each returning instance of the builder itself so you can daisy-chain basically serve as a very flexible constructor. Making one class a friend of another class has it's time and a place and potentially this could be one of those places.

Alternatively, you could define Foo as having one constructor that takes a rather complex set of params, or potentially you could define another class FooData, that FooBuilder could initialize and pass into Foo creation. Then again, maybe Foo and FooBuilder being friends in this case isn't such a bad thing. Just keep in mind that when one class is a friend of another one, you are expanding encapsulation boundary, which could be just as bad as putting more and more code all within one class (i.e. more code knows about internals)

At the end of the day, you could be thinking and considering all these different options and it will all boil down to 60/40. If there's no clear winner, you can always let a coin pick the winner and just go with it. Most likely either one of the design choices would work just fine and by going through the motions and seeing your code in action you will learn valuable lesson for future. Sometimes when I have design decisions and can't decide between A and B, I could end up picking B and then if I ever come across a similar situation I would intentionally pick the other choice. The work in either case gets done and I get the software to do what I want, but you get a ton of benefit of actually seeing your decisions in action and being able to compare the two working approaches, rather than just discussing and thinking about them.