Is it true that if you start having sex at a young age, it makes it harder for you to have kids later on?

No not directly. Sex at an early age has no effect on later fertility, however the more partners a woman has sex with, the greater risk of a sexual transmitted disease. Pid is a consequence and can leave a woman infertile, sterile or even result in a hysterectomy.
Depends. Early sexual activity is often marked by more partners and no concern about STD's or pregnancy.If they acquire gonorrhea, a common STD, that germ likes to feed on the fragile tissue of the Fallopian tubes,leading to scarring and risk of tubal pregnancy or infertility. If they practice safe sex and are monogamous, there is no particular impact on fertility.