7
It means "even though all of them are great writers, your student doesn't know them".
In Russian, и, among other things, means "even".
It can be used in this sense as a standalone word:
Я его и знать не хочу! Я буду мужа любить. // I don't even want to be anywhere near him (literally, "I don't even want to know him"). I will ...
5
It's an adverb. "Если - то" is just like "If - then". You may drop "то", but the phase would lose some of its completeness.
3
The sentence is incorrect and does not make sense as quoted. It probably was intended to be «хотя все они и великие писатели, вашa ученицa их не знает». In that case "и" emphasizes the conditional conjunction "хотя", something like: "Even though they are [obviously] famous writers, your student does not know them".
One might ...
2
To put it simply, the difference is one of emphasis.
When "и" plays the part of a conjunction, it's translated as "and".
But here, it's a particle translated as "even" and it adds an additional stress to the fact stated after хотя.
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