Different meanings. ‘had’ suggests that you might have tasted them, or at least that the fact that you hadn’t tasted them was relevant in the past. ‘Have’ says that you didn’t taste the new foods and that you are interested in the present.

The Past Perfect (had + past participle) is used to describe a past event that happened before another past event. The Present Perfect (have + past participle) is used to describe an event at an unspecified time in the past that has a present impact (though there are other uses) The timeline of the question states you had dinner "last night" and before that past event you had never tried certain dishes. Therefore, the Past Perfect is the correct answer.

HAD is correct. Also, FOODS should be changed to DISHES.

Both are perfect. Use "had never tasted" to emphasize what you noticed WHEN you were at the restaurant. Use "have never tasted" to talk about yourself RIGHT NOW: "I am a person, right now at this moment, who has not tasted many of those foods". It is important to keep in mind that the so-called "Present Perfect Tense" really is a present tense. It talks about the present, not the past. It does not talk about the past except by naming your experiences.

Both are OK. "Have" is the common, basic way to say it. "Had" is the rarer posh way to say it. Both are grammatically valid but have slightly different meaning. "Had" is implying you'd never tasted them prior to that moment. "Have" is implying you've never tasted them even up till this moment (so you didn't eat those rare foods at the restaurant).