To begin with, It is known that Facebook did some multivariate testing on their site (with the delete account page, for instance). Although I'm not sure they did the same with their front page, it is safe to assume this design is based on empirical tests. But that's just an assumption.
The likelihood of people undertaking a task is based on cost/benefit evaluation. Where the more difficult/complex the task is, or the longer it will take to complete, the less likely people are to undertake it.
While you can argue that the first name, last name, birthday and gender are not of functional necessity (they can be presented in a second step or after email confirmation), the form still looks as a low-cost one, particularly considering the current status of Facebook.
Since the cost is low, and in the case of Facebook the motivation should be high upon entry, a single form seems like the optimal solution.
Clustering and Exit Rates
Clustering (in the context of this question - dividing forms into steps, what some call a 'wizard') is a successful technique with complex/long forms. By breaking down the task into smaller tasks, user motivation increases.
Another concept that applies here is that people are more motivated to complete a task once they commit to it (in any way). For instance, an experiment showed higher student turnout when students were asked to write on paper when they will go somewhere (compared to just telling them they need to go there). Or coffee shops giving you a loyalty card with initial 3 coffees ticks (out of 8) has higher commitment rates than those using 1 initial coffee tick (out of 6).
However, clustering has been shown to work better if the users are capable of seeing their progress and evaluate the overall effort involved at early stages. Online surveys show the highest exit rates on long steps, particularly if these appear after short steps and towards the end.
Another example is the hidden costs added to your payment just before confirmation - companies showing credit card subcharges just before payment confirmation have higher exit rates than those spelling them earlier (particularly if these subcharges were above the norm, like in the case of EasyJet, or when the overall purchase cost is low).
The explanation to this is that when users realise that their evaluation was wrong due to interface unclarity (or intentional misleading), they feel cheated. And rightly so.
Does splitting a low-cost registration form into two steps will increase the amount of registrations? Probably not:
- If you don't make it clear it's a two-step, you may make your users feel cheated (even with messages such as "Just a few more details").
- Making it two steps can actually reduce the low-cost nature of the form: users can't evaluate what's hidden.
All of this really boils down to a fundamental UX concept - provide users with sufficient information to satisfy their evaluation needs.
Front Page or Link
It is a momentous business goal for Facebook that people sign up. So the sign up section is really priority 1 on that page - the sign up logo is even bigger than the Facebook logo itself.
The benefit of a link is that it moves content and interactions from the active page to another one - big part of IA. But as just mentioned, nothing is more important for Facebook than people signing up.
Without the form being there, Facebook don't lure you to sign up - you have no way to evaluate how easy it is to do.
Since Facebook (like many other word-of-mouth social networks) don't really have the need to explain what their product does, it leaves very little to put on the front page.
In the process of template slicing, you can classify interaction controls like so:
- Sought Interaction - an interaction control/gesture that executes an action aligned with the action the user wish to perform. For instance, "answer" button on a mobile phone.
- Clustering Interaction - an interaction control/gesture that clearly and directly leads to a template where users can accomplish their sought action. The 'Create a Page' on the facebook front page is an example. If this was my goal as a user, I clearly see an interaction point to achieve this.
- Forced Interaction - This is an action forced upon the user due to the design. In order to accomplish their task, users has to interact with the system at least once in order to get to to the sought interaction. For instance, in an alarm clock mobile app, the need to press 'i' for info in order to then set the alarm (additional step).
Putting a sign-up form and a sign-up button makes the sign up button a sought interaction. A
Register button is a Clustering control - you ask the user to perform an additional step on the way to their real goal - registering.
The Unmentioned Solution
One solution that wasn't references so far is the sing-up/log-in combo - presenting on the navbar email/password field and a sign-up/log-in combo; if the user hasn't registered already, feeling these fields will lead to an additional form (with confirm email, name, etc.).
Although this sounds similar to a 2-step registration, my gut felling is that:
- The two fields still represent low-cost procedure.
- Users will feel less cheated by being redirected to another form.
Unfortunately, at the time of writing I'm not educated enough on the pros and cons of this approach. Various related posts on this site on this pattern might turn useful.
So in conclusion, and in response to your options:
- Ideal solution with low-cost forms, particularly if the business goal is high sign-up rates.
- Conceals the low-cost nature of the form and forces users to perform an additional action on the way to an important business goal.
- The low-cost nature of the form will be concealed by clustering. Clustering in this case will add more noise and cognitive load compared to a single form.The clustering solution is not ideal for these type of low-cost forms.
- In many cases will be considered by users as 'cheating' and could yield high exit rates.
However, all of this can change depending on the context. If your service is a new one, you may prioritise marketing blurb over a registration form. If the site is a flat scrollable one, you may find a register button on a static navbar a better solution.
I hope the answer gives you sufficient reasoning leads. As with many times in UX - there are many variables that could affect the success of a design. The only way to really know in this case is by multivariate testing and analytics.