In 1985, fans of the Hanshin Tigers throew a statue of Colonel Sanders into athe river. In 1985, fans of the Hanshin Tigers threw a statue of Colonel Sanders into the river.

This is past tense so we use "threw" here. "a river" is correct but "the river" sounds more natural to me.

Hanshin Tigers is a baseball team and won the league championship at thate time. Hanshin Tigers is a baseball team and won the league championship at the time.

Your sentence is correct. Here's an alternative.

After that, however, the team faell into poor results and hasn't been at the top inof the Japanese league. After that, however, the team fell into poor results and hasn't been at the top of the Japanese league.

or After that, however, the team fell into poor performance and hasn't been at the top of the Japanese league.

The statue was found in 2009 whileduring river maintenance work and the finder misunderperson who found it mistoodk it asfor a dead body. The statue was found in 2009 during river maintenance work and the person who found it mistook it for a dead body.

We don't usually use the word, "finder," in this type of sentence. This sentence sounds more natural to me.