[Eternal]

Here's my two cents.
Relationships can't be just fun, worry-free and stress-free. Media makes love out to be like that, but its far from reality. Relationships take a lot of work, compromise, and resolution when you fight (and fighting is very normal, just like it would be in a platonic friendship). If you don't want stress, don't get into another relationship. It sounds like you may not be ready and it may be beneficial to just have you-time and do your own thing. Commitment = stress.
As for the girl your seeing, even if she hates your ex that doesn't mean you shouldn't be able to talk to her. Has she told you that you can't? If so, that' s a red flag and you should never have a partner who tells you things you can't do. You should talk to her about this and let her know you're trying to help your ex cope with the breakup, and leave it at that. You don't have to tell her every time you're talking to your ex, but you also shouldn't keep it a secret.
I also want to add that you should try and slowly cut off contact with your ex. If she texts anything mean to you, just don't respond. She's going to be angry for awhile because she's hurt and feels you abandoned her, but it will get better with time and not talking to you will actually help. But its okay for you to still be there if she gets depressed or has no one else to talk to. You can be there as a friend, but you have to be cautious that you're also giving her space so she can move on.