It would be a good fight but i think Bruce wins. He has a large variety of martial arts he knows 127 to be exact I don't know how many Ozymandias knows but probably not as much. Bruce could identify Ozy's style most likely and counter it with something Ozy might not expect ; he may be incredibly fast but Bruce could make it still hard for him to predict his next move.
Yeah but a punch really isn't as dangerous as a bullet or really as quick. It could be countered he could shrug it off. Once he finds out about Nightcrawler's ability he will probably try to adapt to the situation using his knowledge.
definitely catwoman. In the Hush series when she was in the Batcave; Tim and Catwoman got into a breif quarrel and she seemed to be owning for the brief time they fought. And Tim Drake is better than Damian to boot.