How do I go forward with her wanting to talk and be "friends"? Do I avoid her and walk away? If I let her lead, that is where she will lead me... friend zone.
I don't mean to be harsh, but I hear your sense of loss talking here; it sounds to me like you're still trying to affect the outcome, clinging to hope. Time to nip that in the bud.
I look at it like this: My R with my XW is now essentially a business relationship. Like at work where we often have to have functional relationships with people we don't consider friends and don't want to be friends with, yet we still need to keep communication and interaction positive because it's our job...even if we don't like being around certain people.
Same thing here as I see it. Just keep it polite and lightly friendly. When you're ready to be done or walk away, politely excuse yourself. You owe her nothing more than honoring your agreements, keeping things constructive and smooth for your sons, and basic politeness.
I wouldn't worry about telling her about how you want things to be, how you don't want to be friends, etc. I would just define my boundaries by my actions/interactions and leave the rest with her.
About dating: I know everyone is different but I'm going against the grain here and would suggest that you search your mind real good before going on even a casual date. There certainly is nothing wrong with it. But this is a vulnerable time and you are still processing your feelings about your W, your M, the D, etc.
Only you can decide if you're ready or not, and there's nothing wrong with doing it now if you choose. There's also nothing wrong with not doing it until you think you're ready.
