2.  His dad wants to kill him He hopes to have moved his dad’s heart with his pledge, though. Simple Infinitive: to+ verbPerfect Infinitive: to + have+ verb
3.  He loves smoking a good cigar.  He stated having smoked a cigar was relaxing. Simple Gerund: verb that takes a gerund+ verb (ing) Perfect Gerund: verb that takes agerund + having+ verb in past participle
4. 1- He hopes to have moved his dad’s heart with his pledge, though.Main verb: hopes Action To have moved Which happened first? To have moved2- He stated having smoked a cigar was relaxing. Having smoked
5.  Unanimously agreeing, they plunged into the dark. Having agreed on a plan, the group left to fight the unknown. Introductory clauses are dependent clausesthat provide background information or "setthe stage" for the main part of the sentence, the independent clause.
6.  His dad wants to kill him. He didn’t want to be killed. To + be + verb in pp We stopped negotiating the deal with them. The deal stopped being negotiated. being + verb in pp
7.  He was relieved to have been included in the list. To +have + been + verb in past participle He thinks having been taken into account was nice. Hav(ing)+ been + verb in past participle
8.  I want to have a dog. (passive) I called my sister. (introductory phrase) Her boss has called her to the meeting (perfect infinitive passive) (perfect gerund passive)