In the 1890's, the U.S. had the worlds ( 2nd 3rd 4th or 8th) largest navy?

Answer 1

The U.S. Navy dropped out of the top five in the world after the Civil War. The advent of the Spanish-American War in 1898 and considerable support of Theodore Roosevelt who was elected President in 1901 drastically changed the picture.
It is hard to exactly compare navies. Merchant Marine and Coast Guard vessels may or may not be important depending upon the context involved.