In the United States a President is only impeached if it is believed they have taken part of unlawful events. The House of Representatives must reach a majority vote on impeachment and then the President is tried by the U.S. Senate. President Obama would only be impeached if he did something unlawful and the House voted to impeach him.
No, it is very unlikely that President Obama will be impeached, given that he has not committed high crimes and misdemeanors, nor been guilty of treason. Not liking a president is not reason enough to have him impeached or every U.S. president would have faced impeachment due to the people who opposed them. There is thus a very high bar for impeaching a president, and it cannot just be because some people dislike him.
Biden would then nominate someone to be vice-president and if he is confirmed by both houses of Congress he would be the vice-president.
If the President were legally impeached and convicted, the vice-president would take his office and become President. No reason to think that he would be more dictatorial than Obama.
To get impeached the president would have to bribe, lie, or have a misdemeanor against him.
If Obama were to be impeached by the House of Representatives, he would then face trial in the Senate. If he were found guilty of High Crimes and Misdemeanors he would be removed from office and Joe Biden would become President. If his crimes were serious enough, he could then be indited in a normal court if he were not simply pardoned by Biden.
There were resolutions introduced by some members of Congress to impeach President Obama, but none of them gained significant traction or support. Ultimately, no impeachment proceedings were initiated against President Obama during his tenure in office.
If the President is impeached and convicted, the Vice President would succeed him. The Vice President would then assume the role of President for the remainder of the term.
The impeachments for each person would be separate, but they can most certainly be impeached at or near the same time. But that depends on how the House of Representatives wished to proceed - they could decide that handling both impeachment procedures concurrently would be too much all at once.
First Trump would have to commit an impeachable offense (which he hasn't yet), then be impeached by the House (unlikely since it is controlled by the party that nominated him as their candidate), then convicted on articles of impeachment by the Senate (also unlikely for the same reason). If Trump were no longer president then the Vice President (who will be Mike Pence) would assume the office of President of the United States.
They would only if the President were first impeached by the House.
If a president is convicted of a crime by congress, they are impeached. If congress decides toward it, the president must leave office. However, they can veto it. Two presidents have been impeached. They are Andrew Johnson, and Bill Clinton. Also, Richard Nixon would have been impeached for The Watergate Scandal, but resigned before such happened.