Applying the rules of possessive expression

I am now learning to apply the rules of الإضَافَةُ (possessive expression) learned from the previous lesson.

Example 1
Look at the sentences below:

1. كِتَبُ الْطَّالِبِ The book of the student (or The student's book). 
2. عَلَى' مَكْتَبِ الْمُدَرِّسِ On the table of the teacher (or On teacher's table).

By looking carefully at the two sentences above, it can be seen that the مُضَافٌ (possessed noun) can take different cases while the مُضَلفٌ إِلَيْهِ (possessor) can only take the genitive case. This is important to remember.

Example 2
Look at the sentences below:

1. بَابُ الْبَيْتِ The door of the house (or the house's door).
2. إِمَامُ مَسْجِدٍ An imam of a mosque (or a mosque's imam).

Again, by careful observation, it can be seen that:

1. A مُضَافٌ (possessed noun) can become definite when it is attached to a definite مُضَافٌ إِلَيْهِ (prossessor) as shown in sentence 1.
2. A مُضَافٌ (possessed noun) can become indefinite when it is attached to an indefinite مُضَافٌ إِلَيْهِ (possessor) as shown in sentence 2.
3. In all cases the مُضَلفٌ (possessed noun) is never prefixed with article ال.

My comments
Honestly, I find example 2 to be quite confusing because in my mind right now I am wondering how to say the following sentences in Arabic:

1. The door of the house.
   The door of a house.
   A door of the house.
   A door of a house.
   
2. An imam of a mosque.
   An imam of the mosque.
   The imam of a mosque.
   The imam of the mosque.

Can I go for a holiday now? :(