When Lincoln was assassinated, Vice President Andrew Johnson became the new President. No new Vice President was chosen; the office was vacant until Ulysses Grant was elected President in 1868 and Schuyler Colfax became Vice President.
This is why the Constitution was amended in 1967, with the 25th Amendment. It finally set rules for how a new Vice President is chosen when the sitting Vice President has to take over the Presidency.
The U.S. Congress passes bills that become federal laws when the U.S. President signs them (although there are cases in which Congress can make a bill into a law without the President's approval), and each state Congress passes bills that become state laws when the Governor of the state signs them.
There are two heads of the US Senate; the Senate Majority Leader and the US Vice-President. The US Vice-President, who is President of the Senate, only breaks tie votes.
One of the major parties takes over their ideas ^^
US Special Courts or courts of special jurisdiction hear a variety of cases, each related to a particular subject matter. For example, US Bankruptcy Courts hear bankruptcy cases; US Tax Court hears federal tax cases; the US Court of Federal Claims hears cases involving monetary damages against the US government; the US Court of Appeals for Veteran's Claims hears appeals of decisions made by the Board of Veteran's Appeals, and so on. Military courts are also considered special courts.
John Quincy Adams
The President can veto bills passed by Congress, thus checking the Legislative Branch. The President checks the judicial branch by appointing Supreme Court justices.
The primary elections are for delegates to the National nomination convention. Not all states have them and the way in which they select delegates varies. Sometimes the delegation is divided in proportion to the vote, sometimes the one with the most votes get all of the delegates. Sometimes the primaries are only advisory information for the delegates. If no candidate has a majority of the bound and committed delegates by convention time, delegates are all free after the first ballot to vote as they choose. Ballots are taken and deals are made and delegates switch votes until finally one candidate has a majority.