The reason for that is actually inherent to the language itself: in English "then" is used to express both a temporal sequence, e.g. "first study then play" and a logical sequence, e.g. "if he's late, then he'll miss it", and also a general past, e.g. "back then". In Italian "allora" only covers the last two, while for the first one you have to use "poi". In this particular sentence some sort of "if" is implied.

Quindi means 'therefore' which is used in conditional sentences. ex. È notte, quindi accendo le luce = It is night, therefore I turn on the lights.

Qui/qua both mean here, while lì/là mean there; and for the record, there's also costì and costà, but you'll likely never hear them outside of Tuscany.

The meaning of each is as follows:

• Qui: right here where I am
• Qua: in my general proximity
• Costì: right there where you are
• Costà: in your general proximity
• Lì: exactly over there
• Là: over there

In actual speech, most Italians don't mind the difference between qui and qua and between lì and là that much, usage depends more on personal preference; when in doubt, use qua for here and là for there, they're the most common, especially in idioms.

There's no mai in this sentence

So did I and the correct answer was "Allora perché sono qui", which pretty much confused me.