2nd Paragraph

Translation

ὁ Δικαιόπολις ἔκοψε τὴν θύραν, knocked on the door

ἔκοψε, he knocked, simple fact
ἔκοπτε, was knocking, kept knocking
We're not interested in the duration ἔκοπτε, imperfect
but in the simple fact: What did he do [then]? - He knocked. ἔκοψε,aorist
Besides past augment, there is always a stem change to indicate aorist, simple aspect.
 

ὁ δὲ ἀδελφὸς ἐλθών... ἰδών.... ἔφη.. His brother came.... saw... and said... [= having come, having seen, said]
We could have said:
ὁ δὲ ἀδελφὸς ἦλθε... εἶδε... ἔφη 

The Greeks preferred using participles:
Coming (or: having come), seeing... he said...
Aorist participle does not indicate time but simple aspect. What happened next? Consider:

Dikaiopolis knocked on the door. Simple aspect, specific action, aorist.
His brother came to the door. Simple aspect, aorist.
He saw Dikaiopolis. Simple aspect, aorist.
He said: Greetings! Simple aspect, aorist.

This succession of simple aspect actions can be made more elegant by using participles. But we must use aorist participles to retain this simple aspect characteristic.

Compare:

Going to the door he said to his wife: I'll see who that is.
   ἰὼν (= ἐρχόμενος) πρὸς τὴν θύραν for progressive aspect: while going
Going to the door he opened it and said: Oh, it's you.
   ἐλθών πρὸς τὴν θύραν for simple aspect: he just went and then...

εἴπετέ μοι tell me!

Aorist imperative for simple aspect specific commands: tell me once and for all
εἰπέ μοι: tell me! (order given to one)
Tell me, once and for all, something specific, not a general:
λέγε speak! (and go on speaking OR speak in general about general things)
ἐλθέ come! (now!)
ἰδέ Look! (quickly! now!)

ὁ δὲ παῖς, ἰδού, τυφλὸς γὰρ γέγονεν.  the child has become blind.

completed aspect: Perfect tense: as a result he sees nothing.

 Compare 
simple aspect: What happened next? He fell and [then] became blind.
simple aspect: ἔπεσε καὶ τυφλὸς ἐγένετο (Aorist tense)
progressive aspect: Night was already falling (Imperfect tense)
simple aspect:    νὺξ ἤδη ἐγίγνετο 
simple aspect: Night is falling. (Present tense)
simple aspect:    νὺξ γίγνεται.
simple aspect: Night has fallen and it's now dark. (Perfect tense)
simple aspect:    νὺξ γέγονε καὶ σκότος ἤδη ἐστίν.
 

ὁ δὲ ἀδελφός, ἰδὼν τὸν παῖδα τυφλὸν ὄντα, ἔφη...
When he saw what exactly? simple, specific fact: The child is blind!
So we want aorist tense: εἶδε τὸν παῖδα τυφλὸν ὄντα. 
So we waor aorist participle: ἰδὼν τὸν παῖδα, ....

 Note the difference between: 
ὁρῶν τὸν παῖδα, ὦ Ζεῦ, ἔφη , ...
   Looking at the child he said: Good grief, ....
   He said this while looking at Philip
versus ἰδὼν τὸν παῖδα .....
   Seeing the child (= He saw the child and then said...)

τί ποτε ἔπαθεν ὁ παῖς;
What (exactly) happened to the child? Simple, specific fact = simple aspect
So:

Whatever happened to you? τίποτε ἔπαθες;
   Me? Nothing. οὐδὲν ἔπαθον 
What happened to all of you? τί ἔπάθετε; 
   Something terrible happened to us. δεινὰ ἐπάθομεν 
 

τί ἐγένετο; Whatever happened? Aorist simple past fact, versus
τί γέγονεν; What has happened? Perfect (with what result?)

ὁ Φίλιππος δεινὰ ἔπαθε.
τυφλὸς ἐγένετο. 
πῶς τυφλὸς ἐγένετο;
οὕτως. This is how:

ὁ Φίλιππος νεανίας τινὰς εἶδε μαχομένους.
προσῆλθεν.
μὴ τύπτετε τὸν τλήμονα, ἔφη .
εἷς τῶν νεανιῶν ἐνέπεσε τῷ Φιλίππῳ.
ὁ Φίλιππος πρὸς τὴν γῆν κατέπεσεν.
Result: νῦν γε οὐδὲν ὁρᾷ
     τυφλὸς γὰρ γέγονεν.
Perfect tense: The child has become blind = is blind

 

Aorist imperative
κόπτουσιν τὴν θύραν. τί λέγεις; 
     τίς ἐστιν;
        εἰσελθέ (to one person)
        εἰσέλθετε (to several)
οἱ δὲ οὐκ ἐθέλουσιν εἰσελθεῖν ἀλλὰ καλοῦσίν σε ἔξω λέγοντες· ἐξελθέ σύ. No, you come out! (if there's only on of you) or ἐξέλθετε ὑμεῖς (if there are more of you)
εἰπέ μοι τί βούλει Tell me what you want (singular)
εἴπετέ μοι τί βούλεσθε (plural)
Why are all these imperative forms aorist ?
    Because they are all simple, straightforward, specific "once" orders.