The implication of "I visit them often enough" with "in a sufficient amount" is also implied by 經常 and 常常. There are times that you cannot translate every single word to convey the full intent. This is cultural biase. In this example, "enough" need not be translated. If you do, then the target translation sounds unnatural and even weird. However, if you want to emphaise "enough" in the translation, then more is needed. For example, I visit them often 我 經常 探訪 他们 enough, 已經够了. Without context, this sort of emphasis in translation can be construed as having a grudge.

These two words can express the meaning of "often",but“常常” is usually used in spoken Chinese while"经常"is more formal.When we write something we usually use"经常".Besides,"常常" is more like"frequently".But generally you can use both words when you refer to "often."

These two words doesn't have much difference . You can use neither of them in the sentence you mentioned

I think your two examples with 'enough' have some underlying meaning for you and the one you speak to. I write often enough, enough for what? You didn't say. So the translation become difficult.