If Qui Gon hadn't been involved with the Trade Negotiations

1. and never ended up finding Anakin would the Emperor have succeeded with his plan of taking over the galaxy ?

Yes, Anakin was not that important. If Anakin would not have turned, Dooku or even the Clones Troopers had finished the job well. I guarantee it.

2. How would have things been different ?

If it was the "will of the Force" like Qui Gon believed (but he is a maverick Jedi with his living force concept, not the prevailing opinion) Anakin would have be found by someone else.

If Anakin would not have been found there would not be balance in the end...uh, strike that, Rey Palpatine-Skywalker-Organa-Solo would have brought balance anyway.


3. Would it have been Darth Maul as his sidekick the whole time ?
Yes, unless Dooku as new candidate had defeated Maul in a apprentice duel as is Sith-tradition.