am I able to heal on the way to petalburg for the first time

you shouldn't heal there, you should potion a tile before the grass in the next route. It saves more time to do like this anyways

But if you take a little to damage on Rival fight you can heal at your house for safety(mainly if you are below 7 HP after Rival Fight
But it is only mentioned in the old route no idea about the new route you should probably ask in Gen 1-3 Pokemon Speedrunning Discord server