Your prompts are very broad and a discussion based on them is open to generalizations that may not apply to the people you eventually end up working with.
You are far better off discussing these questions with the people you intend to have around you when you start your new venture.
You projected your desire of getting work done onto the company's desire to keep people working.
Full time employees need to be 'busy' all of the time to justify investments the company makes in each person (opportunity to learn on the job is the biggest investment). If you go there and finish all of the work, there won't be anything left for the FTEs to do.
You're better off giving FTEs (full time employees) learning opportunities and telling them they are really bright.
And don't burn bridges - just fake it and pretend to be nice - life sometimes works out in really strange ways.
It is a problem for freelancers - people always ask for free solutions to real problems and various ways. Candidate employees are in the same situation, but during the worst possible time - the interview.
As you said, you want to hire people for whom solving your problems is easy. Keep in mind that your problems are not unique and probably already have a solution, so you really need someone that.....woops...almost gave it away ;)
Liberation is good - Google is good - so are privacy agreements.
A better name for the site could be "Grab a Copy of Your Data!" - much more accurate. Liberate implies that you are actually getting your data back - which you're not...you're getting...a.....copy.
You should not hire people that do any of the things you ask. They are giving their valuable services away for free - since your company exists to make money, your employees giving their time so freely is likely to affect your profitability.
People thinking about applying - Reconsider. The company is too cheap to pay for good work - they extract what they need from interviews. Its likely that you'll never discuss pay with them since you're not going to get hired once they have their answers.
(the details)
Getting work done in an interview is a poor practice since the candidate does not know if the work relates to an actual problem or is fictional.
If an actual problem, you are asking for the candidate's time and could end up using the candidate's approach - this puts you into a conflict of interest: you have a candidate that just gave you what you need and you are in a position to hire.
If the problem is fictional, why bother? How does it help?
Besides, candidates are smart too: it's likely they hacking the interview process too. Not sure where that leaves anyone, but good luck with that.