Kindly tell are all sentences meaning same?

Not without a that after problems!

By the way, why the plural, democracies? A country that practices democracy has a democracry (system), not multiple, isn't it?

(Edit: my comment applies to #2. I didn't notice you had two choices. #1 sounds OK to me though the passive is, I think, not necessary)

Hi, 

Perhaps they are talking about the democracies that exist in two different countries, eg The USA and Canada?

Best wishes, Clive

Thanks for correcting me, GG. I remember it was different when I read it yesterday. My mind must have been playing tricks on me.

2. In some ways, Obama’s candidacy illustrates the problems our democracies faces today

Just change 'faces' to 'face' or even better, 'are facing'