Yes, every act of intercourse should share in an intention of fruitfulness.
NFP, rhythm methods, or any other form of birth control would violate your logic.
Yes they would if they were used to prevent conception of new life without a corresponding grave reason.
Also, people that can not have children should be forbidden to marry.
Yes, impotence has always been considered an impediment to marriage. Sterility has not because who can ever say for sure that someone could not conceive. The examples of Sarah and Elizabeth have probably influenced the magisterium towards caution on claiming that someone could not have children. But they must at least be able to complete the marriage act.
Just because I said that sex in marriage is primarily for procreation doesn't mean that there is not a secondary feature which is the intimacy between husband and wife. There is nothing in the Bible or Catholic teaching which says that an infertile couple may not have sex. God is the only one who should have control over who is sterile or who is not due to and act of nature i.e. something inherently wrong in a man or womans reproductive system. There is nothing wrong with a couple who is more infertile to try drugs to enhance there reproduction however, the Catholic Church teaches that when you disrupt the marital act and try to grow a baby in vetro fertilization thise is wrong because it is outside of the human act of the partners and involves the performance of the act without the consumation of the man and the woman as Jesus said becoming one flesh.
Infertility among people is within at the least God's permissive will that some people are sterile. He has his reasons for permitting this.
There is nothing wrong with my logic. Most people before they marry do not know whether they are sterile or not. If they knew before they really got into a more serious courtship they may say well I want children and this person can not give me children and will not adopt so I will not develope my relationship with them. Most people do talk about children before they get married because they want to know how the other person stands on this important issue. The average person, however really doesnt know if his future wife is fertile or not. Most people leave this up to God's providence also. God has put in mankind the natural desire to want to reproduce offspring. I speak in generalities- there are always people who do not want to have children and it seems that more and more people are opting out or limiting their families to one or two. This is sad because we are not even maintaining our population. Particularly in Europe. We were sold a bill of goods that the population was exploding in the 1960's and many people still buy into it today.