The church is chosen by God. But the church did not replace Israel. The church is the fulfillment of the reason God chose Israel as His elect nation. And just as God chose Israel to be a blessing to the world, so also, the church, as the elect people of God, are to be a blessing to the world.
The basic explanation of Unconditional Election is that God, in eternity past, had an eternal decree by which He predetermined all things that would happen. This post provides several unconditional election quotes from Calvinistic authors and pastors. It is important to let Calvinists define election in their own words.