The correct answers are How long have you known him? and How long have you liked him?

We use the present perfect ("have" + past participle) with "how long" to ask about the duration of an ongoing situation that started in the past. Because "know" and "like" are state verbs, we use the simple present perfect rather than a continuous (-ing) form. "How long do you know him?" is a common mistake that incorrectly uses the simple present tense.