If you want to travel from Finland to Estonia, you have to include a ferry on the route from Helsinki (Finland) to Tallinn (Estonia). Daily ferry connections are available which take about two to three hours.
To travel by train from Finland to Russia, you have several direct day trains from Helsinki to Saint Petersburg. And one direct night train from Helsinki to Moscow. Book your train ticket via one of the given booking links.
To travel from Finland to Sweden, you have two main routes. In the South by ferry from Helsinki or Turku or Stockholm. In the North by bus from Kemi (Finland) to Lulea (Sweden). There are good train connections available to Helsinki, Kemi, Turku (Finland) and from Stockholm, Lulea (Sweden) onwards.
Don't miss the excellent night trains in both countries.