(a) The patients are waiting for seeing the doctor.
     The patients are waiting to see the doctor.”

The second sentence is correct.

(b) It is cheap to travel by bus.”

This sentence is correct.

(c) Tourist often buy souvenirs to take back home.”

Change "Tourist" to "Tourists."

(d) Deserts are covered by / with sand.”

Either is correct.  Using "by" emphasizes the act of covering the desert (and implies a source or cause of that act), while using "with" emphasizes the sand itself.

e) He is admitted to hospital due to / because of (a) high fever.”

Either "due to" or "because of" is acceptable.  The indefinite article ("a") is not required here, but it sounds best if it is used.

(f) The computer makes our lives / life easier.”

It should be "lives."

(g) The tourist is asking for directions.”

This sentence is correct.

h) She asked Jenny to watch a  / the film.”

Either article can be used.  The indefinite article ("a") suggests little importance to what actual film she is watching, while the definite ("the") would make it clear that you are referencing a specific film.