No, you didn't. It's こんにちは (same 'wa' as the topic particle - this greeting is originally a phrase though it's treated as word now); also you can't use 新しい like that. You probably want to use 始めた as an auxiliary verb to say this.
I can't think of any reason that '正しく言ったか' would be wrong but I don't think anyone actually says that either, it's probably quite unnatural. It'd be simpler to just say 「正しいか」 but you could say 「言ったことは正しいか」 to be quite explicit.