This year (2010) there is no presidential election. In the last election, the majority of US adults voted for Barack Obama - and he is now President.
It remains to be seen who will be nominated for president in the 2012 elections although it is presumed that the incumbent will secure his party's nomination if he is eligible to run - which Obama will be in 2012 unless something unexpected happens. Recognizing the current widespread popular opposition to Obama's most significant government initiatives - and the backlash against them expected at the polls tomorrow (2 Nov 2010), it is not certain that Obama will seek reelection (although it is expected) or garner his party's nomination (although it is likely he will).
by voting
They vote because they have an interest in the outcome of the election and because they believe that voting is a duty of citizenship.
2 terms or 4 years
18 is the legal voting age in the US.
by voting as it is a republic nation
voting in presidential elections
That is correct. US Territories can not vote for the US President.
it expanded the definition of citizenship to include voting rights for younger adults
no
That is the correct spelling of "elector", a voter or voting representative, especially those chosen to elect a US President and Vice President.
In the US, you should check with the local country voting registrar.
she is voting for barak obama