If President Donald Trump were impeached and convicted, and Mike Pence became president, how long would his term be? Would it be for 4 years or would there still be a 2020 election?
There would still be a 2020 election
If a President is impeached and removed from office, or stops being the President for any other reason, the Vice President serves the remainder of that President's term, according to the 25th Amendment to the Constitution.
The 25th Amendment has been tested under Richard Nixon. Although he was not impeached, Richard Nixon resigned amid the Watergate scandal, and his Vice President Gerald Ford became the President in 1974. Gerald Ford served out the remainder of Nixon's second term, and ran for President in 1976, losing to Jimmy Carter.
The United States has presidential elections every four years. Absent some near total calamity like a nuclear war that prevented communications from occurring, there will be a presidential election in 2020. Impeachment does not interfere in that process at all.
If Donald Trump were impeached and blocked from running again (which is one of the things that impeachment can do, disqualify from office), then Mike Pence would serve out the remainder of his term. Pence could run in 2020. Pence could run again in 2024, as even if he won in 2020, he would have been president for less than six years by inauguration in 2025.