Hello.
"идти по выставке" - we can't use this preposition here, it is incorrect. You can use only "на" and it means that you are going to visit some place ( выставка, конференция (confernce), мероприятие ( event) etc.). So you have intentions to visit something or you are already goung there.
But let's take this example: идти по стадиону-идти на стадион. So the second one it is an intention to visit a stadium( or you are in process of going there), but the first one it is a process of going (already) inside this stadium, so you are already there! Идти по дороге - to go on a road ( you are there). "Выходи/Иди на дорогу" - you are are not there , but you are going to be there.
The same cases we can dind with "В" and "По": идти в музей ( not yet there), идти по музею ( alredy there, to be in process of seeing pictures in this museum, for example)