Your examples show a narrative with mixed first- and second-person narration.
But let's clear up second-person narration first.
Second person narrative is what it is called when the main character is being addressed directly. It is marked by frequent use of the word "you." (Chris Sunami)
A clear example of pure second-person narration is Bright Lights Big City by Jay McInerney which begins:
You are not the kind of guy who would be at a place like this at this time of the morning. But here you are, and you cannot say that the terrain is entirely unfamiliar, although the details are fuzzy.
The novel continues to be told firmly in the second-person. (Go to Amazon and read the first two chapters in the preview to get a feel for what second-person narrative can be.)
Now that we know the difference between third- ("He went ..."), first- ("I went ..."), and second-person narration ("You went ..."), let us analyze your examples.
Your example shows a mixed perspective. There are two characters here, the one narrating from a first-person perspective and the other person, addressed in the second person, who is being asked and who answers.
It is important to note that in your examples the second person is not the reader! The reader does not take part in the story. The narrator can address the reader ("Dear reader, ..."), but the reader cannot act in the story. In your example, the "you" takes an active part in the story: "You think about it for a while and then you tell me you are hungry and that you first want to get some lunch." The reader cannot tell the author that they are hungry. So this "you" cannot be the reader.
I don't know how this story continues. It could be that the first-person narrator steps back from the story completely and tells the adventures of the second-person viewpoint character ("you"), turning this into a second-person narration. Or it could be that the second-person character sits down over lunch and remains there while the first-person viewpoint character goes on an adventure, turning it into a first-person narration. Currently it is a mixed viewpoint narration, and it could well be that both the narrator and the audience go on an adventure together.
However that may be, the general schema for a narration is this:
v | real world
narrator audience <----+ "frame" fictional world
| ^ |
| | |
(narrates) (hears) may or may not be identical
| | |
v | |
1st-person 2nd-person |
viewpoint and/or viewpoint <---+ "story"
The author writes the book in the real world. In the book, the story is told by the narrator. The narrator may or may not explicitly appear in the book. If he appears, it can be in a framing narrative (such as someone telling a story to an audience or someone remembering his past), as the protagonist (who narrates the story as he lives it), or as a side character (who observes the events from within the story, for example as a companion to the protagonist or as the antagonist). The viewpoint character is a part of the story, either as its protagonist or as a side character. The viewpoint character can be identical to the narrator ("I went ..."), to the audience ("You went ..."), or a different person ("He went ..."). Like the narrator, the audience can explicitly appear in the narrative (as a second-person viewpoint character or as the listener in a framing narrative) or he can be implied. When the narrator addresses a reader ("Dear reader ..."), in fiction this "reader" is not the real world reader of the book, but the audience: an instance of the text. (Only in non-fiction does the author actually address the reader directly. In non-fiction there usually is no narrator and audience ["I'll explain to you how to bake cake. You take a cup of flour ..."].)
Examples to explain the narrative instances
In your examples, the "I" is the narrator and the "you" is the audience. Let us look at some other examples to hopefully explain the narrative instances better:
An author writes a story, in which a storyteller sits down with some children and tells them a tale. The storyteller is the narrator of the tale, and the children are the audience. Both are fictional characters inside the framing narrative, and both do not take part in the story that the storyteller/narrator tells. You, the reader, read the book. The storyteller will address the children with "you" and speak of himself as "I":
Listen, children, I am going to tell you a story.
In that example, the "you" refers to the audience (the children) not the reader, but both narrator and audience are not part of the story.
Listen, children, I am going to tell you a story. There once was a man and he ...
Now we can change this book so that the narrator tells his own story to the children. He will tell the story in the first person, and the "you" is still the audience, and neither the reader nor a character in the story. (And the narrator is not the protagonist either! He tells his own story, but looking back on it, so there is a temporal difference between the narrator and the protagonist.)
Listen, children, today I am going to tell you a story. Yesterday I went to ...
But now we can go a step further and imagine that the narrator, on August 31st, 1953, tells the children the story of how he and the children went to Coney Island on August 30th, 1953 (and you write about that and I read it). Then, both the "I" and "you" are characters in the story as well as characters in the framing narrative. They are both protagonists – a first-person and a second-person protagonist – in a mixed first- and second-person narration.
Listen, children, I am going to tell you how we went to Coney Island and you ran away and I had to search for you.
And of course you can leave the framing narrative away, and then we have an example similar to yours, where the narrator and first-person viewpoint character are identical and the audience and second-person viewpoint character are identical as well:
Yesterday we went to Coney Island and you ran away and I had to search for you. You all cried, because you were afraid, but when I came, you smiled, because I brought you ice cream. Then we got on the bus and rode home.
Difference between mixed first-and second person narration and first-person narration
The previous example (and your examples) are not first-person narration! The following is first-person narration:
Yesterday I went to Coney Island with the kids and they ran away and I had to search for them.
Mixed first- and third person narration is rare
Whether it is mixed first- and third-person narration will depend on whether we have a head-hopping narrative in which the third-person has its own viewpoint (with an internal view of the third-person character: "I thought/felt ..., and she thought/felt ..."; this is rare and generally considered bad writing) or merely a side character (with only the first-person viewpoint character's outside view of them: "I looked at her and wondered what she thought."; this is common first-person narration).
There are no different terms for second-person or mixed narratives in different tenses. You could say: mixed first- and second-person narrative in past tense. But that is not a term but merely descriptive.
Different kinds of narration can be distinguished by point of view – that's what you are asking about –, voice, and time. They are all explained in the Wikipedia article on narration.