Your English is wonderful. There is one grammatical mistake in sentence three but the rest look good to me!

1.The tangible project was set up under the aegis of this institute.

2. They have long been involved in a crusade for desegregation.

3. The clergyman had relished to deliver theological sermons to local people.
*This is using two different tenses and could be re-stated as:    
a) The clergyman relished the idea of delivering theological sermons to local people.
b) The clergyman relished delivering theological sermons to local people.
c) The clergyman relished delivering theological sermons to local people.

4. The revelries next door kept me invidious all night.

5. He has earned the moniker of "King of Lizard" by cellmates.

6.They pleaded that the conclusion she has drawn are based on a false premise.

7. The expedition of the dance troupe to London is leaving next month.

8. The aristocratic family life shown here is not normal, it's a perversion.

I really appreciate your help!

Etsuko