Actually, it is an impeachment hearing. There is no requirement to bring it to a vote -- no vote was taken on the Nixon impeachment hearings until months after the investigations began.
What election? The Presidential election isn't until next year and the Democrats state they want Impeachment proceedings concluded before the end of the year. Even if they aren't finished, it is highly unlikely that the House will still be working on impeachment a year from now -- before the election.
And this would be false. There appears to be little doubt that the House will be impeaching the President. The question now is if enough Republicans will find their conscience and vote to convict in the Senate.
Yes, with Nixon there was a vote several months after the impeachment investigation started in the House, being done in closed session by committee. Further, it is odd that the rules that the committee are following are the same rules (closed hearings and all) that Republicans created during the Obama administration, to investigate his administration. It is odd that Republicans are whinging so much because they are now the minority party having to abide by the rules they created -- and if they are "Soviet style secret courts," they are that way only because Republicans made them that way.
As for Clinton, they got the information from the Ken Starr's investigation -- the House did not have their own impeachment investigation, so there was no vote before the investigation started.
Further, investigations are largely always secret. If the police are investigating a crime, they do not invite the press, or the suspects lawyers along to watch them investigate. In fact, law enforcement (as a general rule) typically won't answer questions about investigations. As others have pointed out, when Clinton was being investigated by the Republican House, those hearings were secret.
Now, when they start working on articles of impeachment and call witnesses in support, or to defend the President against, those articles -- those will be open hearings.