Your understanding of the past perfect is close but not 100% correct. We use the past perfect to indicate an event earlier in the past was completed relative to another time in the past, not just to indicate that one came earlier. For example, in "I ate dinner and fell asleep", obviously eating dinner came first, but you don't need the past perfect. Saying "I had eaten dinner when I fell asleep" says that the act of eating dinner was already complete at the time when you fell asleep.
In your sentences, you're not actually stating anything relative to anything else, although I realize it looks like it. When we use the past perfect, we often use a word like when or before or although to indicate a relationship between the two events. To use the past perfect, you would have to rephrase the sentences like this:
a) I had explained it to him thoroughly, but he still made a mistake.
This indicates that the explaining was already complete before he made a the mistake.
b) I went to the mall yesterday and there I unexpectedly met my teacher.
This one actually doesn't need the past perfect, because saying "I had gone to the mall and there I met my teacher" suggests that going to the mall was complete before your met your teacher, which is not what you mean. If you mean specifically "the act of travelling to the mall" was complete, you could say "I had driven to the mall", but this is a quirk of English usage.
c) I had already parked my bike near xyz when I saw the No Parking sign.
This is a more idiomatic way to phrase it. As I said, we don't use the past perfect just to indicate that one thing happened before another, but to indicate that something was already complete before another event. In this case, your parking was complete before you saw the sign.
d) I called him in the morning but he did not pick up the phone.
Again, this one shouldn't really use the past perfect. Using the past perfect would suggest that you calling him was complete before he did not pick up the phone, which is not what you mean: he did not pick up the phone when you called him.