I didn't complete the tournament and knockout in simulation mode. But I search on the internet and here says that if you beat tournament and knockout in simulation, you unlock advanced options. http://www.cheatcc.com/psx/codes/nfs3.html But I think it will not unlock anything. And the person who writes this probably confused simulation with arcade mode.

The advanced option is only available in simulation mode. And it is not necessary to beat tournamant. Put the game in simulation mode and when you are selecting your car, above or below show case there is settings. When you enter it will appear advanced optons. This is only available in PS1 version.

Horsepower is a cheat to increase the acceleration of the car. To use is, you need to press some buttons after confirming the race and during the load screen.

Well, the best way I found to prove that we are not cheating is to record and play at the same time. But not everybody has a good pc to play and record at the same time. In my case, I changed the video record in these two videos:

Hometown 1:00.75 Atlantica 1:28.78 in lap 3