Widespread exploration was made possible in the 1400s by the growth in wealth in Europe as well as new technological developments in ship building that made traveling far distances more attainable. The political regimes of Europe became more centralized at this time and were able to raise more funds to help support the acquisition of new trade routes and territories around the globe. New ships were built and developed at this time that also allowed for further international travel. Hope this helps!
The answer to this varies for each of the branches. The people are most directly involved with the legislative branch and least involved with the judicial branch. The people are directly involved with the legislative and executive branches in that they vote for the people who are the leaders of those branches.