Simple logic- the symbiote hangs around Central Park then latches onto Peter. That's all the quote says. You misread it as "after he takes it off". All it's saying is that it first appears in Central Park and that the first appearance of Venom is later down the road.
Debateable, if the leak of Peter being 'infected' is true. It would mean that the teeth, tongue and claws are a part of the symbiote fully taking control and not something unique to Brock. We just see him embracing it more than Peter.
Harry is covered in bladed weaponry. Venom gets 'shanked'. Some will say differently, but I would just put two and two together.
That's a technicolor way of looking at it. Brock prays for Peter's death in a church dedicated to God way before he finds out Peter is Spider-Man or has the symbiote drop on him. He then proves how lacking in upright morals he is by fully embracing the 'infection' of his body, not once resisting it. There's no victim in this, just an unholy union between two power-hungry beings.
The point I'm trying to make is this- Brock didn't ask for the alien symbiote nor did it ask for him, and when you really think about it how long would it be if he didn't have the symbiote until he decided to take matters into his own hands? He's a man lacking a conscience, and if this were a normal situation between normal people there's only so much a man like Brock would take until he picked up the nearest six-shooter and tried to shoot Peter right between the eyes. The only difference in this case is that he has an alien symbiote fall from above that offers the power he needs to take out someone like Peter.
smiley here]
