There are long term studies of unemployed in multiple countries that have social safety nets that would be worth reviewing (for example: http://amzn.to/1nosUtx Cultures of Unemployment: A Comparative Look at Long-Term Unemployment and Urban Poverty published by Amsterdam University press in 2006) For many the impact of unemployment (for instance following closure of UK coal mining and steel industries) its not just the loss of job in the economic sense, but the disconnect from the workplace, community, changes in sense of self-worth for individuals and long term cultural and regional impact. There are proven strategies that work and lots of examples that failed. Learning from these and seeing which opportunities map to actions that start-ups can effect through mobile, social and learning technologies might be a useful starting point.

Will this be possible to simulate if the participants know they are taking part in a study?

And in particular, if they know they cannot count on the basic income indefinitely? Studies on this in the past have hit that exact problem.

I think if a basic income is eventually introduced nationally it will be the result of a hard-fought political battle with many proponents and detractors, and there are plenty of cases of laws like that being reversed within a few years.

I don't know this would be too unrealistic for the study.

Studies typically have a set duration. If you offer people a basic income for the duration of the study, they'll need to plan differently than if they have some reasonable chance of having a basic income indefinitely.

This is certainly true. However, for many cases there may be little difference. A year or two of basic income is sufficient to start a business, learn skills to enable a career switch (exceptions, of course), care for a newborn, deal with short-term illnesses, etc.

That's always a hard thing to tease out of psychological studies. The tests have to be very clever to do so, and they'd have to be wide ranging. Essentially, yes, but it'll cost a lot of money.