This question was asked some months ago, but with rather meager responses.
There have always been "third parties." But in general they have been marginal. The existence of a legitimate third party has almost always been a sign that one (or both) of the two parties is going through significant turmoil. It has actually been common to divide the history of the US into periods of "Party Systems," based on which two parties are dominant.
You will note that some of these have little interregnums. Between the First and Second system there was basically single party rule under Jacksonian Democrats. Between the Second and Third was a bit of confusion as the parties realigned themselves. The Whigs collapsed. And briefly a bunch of parties flourished before the Republicans created a coalition of Whigs, Know Nothings, and disaffected Democrats. While the Democrats swung to the hard right and dominated in the South.
After that the changes in the party systems were made by re-aligning existing parties. Martin Luther King didn't form a new party for civil rights. He got the Democrats to do it for him. Which led to the Republicans swinging Right to counter and resulted in the Sixth Party System.
In all cases the US political system tends to naturally devolve into two parties. The single district, winner takes all, form of election all but ensures it. There have been exceptions of course at all times. But it is really hard for small single issue parties to win any election against a large broad coalition party. So most single issue voters have always tended to vote for the other broad coalition candidate that kind of supports their cause rather than a third party candidate.
No. The Republican and Whig parties were contemporaneous (with the Democratic Party) as the former rose and the latter fell. The Populist Party existed along side the Democrats and the Republicans, as did the Progressive (or Bull Moose) Party