1. She reached  the hospital although the  snow was falling  heavily.

Rewrite the statement using 'despite'.

Answer: Despite the heavy snowfall, she reached the hospital. OK

2. Fill in a preposition:

The leader spoke with the heads of the followers. OK grammatically. But 'heads' is not a good word to choose, since it essentially means 'leaders'. ie 'the leader spoke with the leaders' sounds odd. But the grammar is OK.

3. Fill in the correct form of the tense:

 They __________ (live) in this house since 1993.

have lived.

But I think have been living is better. But the real question is whether 'have lived' is grammatically wrong? Please  reason out in order that I may understand. Both tenses are correct grammar. The continuous stresses more the uninterrupted nature of the activity, and the length of the period.

Best wishes, Clive