Speaker/Majority Leader sets the rules and agenda, REDSTATEWARD. Something routinely demonstrated in the Senate, where I am guessing you have little problem when that authority is used.
Pelosi, in this case, following rules put in place partially by John Boehner. Again, presumably given the (R) by his name that was ok with you at the time.
No, Pelosi can't declare the President impeached. Yes, she needs to call a vote for that. She doesn't need to call a vote to open a lawfully recognized and constitutional inquiry.
As a federal judge ruled just a few days ago.