"Payment over the internet isn't always safe. Payment on the internet isn't always safe. Paying over the internet isn't always safe." These are natural. "Paying on the internet isn't always safe." This one sounds unnatural to me, it's grammatically correct, but I would never say it. Also, you don't need to say "online" because you're talking about doing something on the internet (it implies that you're already online)

Online payments are not always safe. / It is not always safe to pay online / Paying over the internet is not always safe. When you use the word 'online', you do not need to add 'internet' in the same sentence.