I missed two days of classes and an important football match for the school team.
1) Before that, I HAD NOT MISSED (why not "had not been missing"?) a day of school for two years.
It is past perfect tense, which means that something had happened AND FINISHED BEFORE an action IN THE PAST.
She the key is "HAD FINISHED" by the time the action in the past (missed 2 days of classes) occurred.
Anyway, I passed my driving test! 2) I HAD BEEN TAKING ( why not "had took"?) lessons for six months, so I`m glad I finally have my license.
You mean: "Why not "had taken"? (Past Perfect) because there is no pattern using "had took"
It's because it is Past Perfect Progressive Tense. This tense is used when you want to express actions, more likely longer actions, or situations that were in PROGRESS before some other actions or situations in the past.
The number 1) doesn't use Past Perfect Progressive Tense I think because "Miss" is a stative verb. Some verbs (called stative verbs) are not normally used in the progressive form.
e.g. know, like, understand, believe, hear, etc.
I was happy to hear you`re going to Paris this summer. 3) HAVE YOU BOOKED (why not "Did you book"?) the ticket yet?
We must you use Present Perfect Tense for this sentence because the question mainly focus on the action "booked", whether you have booked or haven't booked yet.
We don't use Simple Past Tense (Did you book) because if we want to use Past Tense, the main focus should be for the TIME.
Here is the right usage: Did you book the ticket YESTERDAY?
So, it emphasizes the time. That's when we use the Simple Past Tense
But for your question, it doesn't emphasize the time in the past, but only focus on the action. So Present Perfect Tense is used.