Is a wife entitled to object to and prevent conception despite her husband's desire, given that she gives birth via C-section and suffers pain during and after childbirth? And is it permissible for the husband to marry another woman for the purpose of procreation?

Procreation and increasing offspring are a legitimate aim of marriage, and it is a right for both spouses. Neither is permitted to abstain from it without the other's consent, except for an excuse. What you mentioned about your wife's pain from the cesarean section permits her to space out pregnancies and childbirths using temporary birth control methods, but it does not permit abstaining altogether. The Islamic Fiqh Academy emphasizes that a law limiting procreation is impermissible, and sterilization is forbidden except out of a legitimate necessity. Temporary birth control is permissible for a need deemed legitimate by Sharia, with the agreement of both spouses, and using a permissible method. As for your marrying a second wife, there is no sin in it as long as you are capable of being just.