Are infrequent periods a sign of infertility?

Could be. Depending on the cause for infrequent periods you might have trouble getting pregnant. Please see your doctor. If you're not trying to get pregnant appropriate contraception is still necessary.
Probably. You should have regular cycles each month. If you try over the counter ovulation predictor kits and they do not show ovulation, then you do need to consult with you physician. There are tests that can see if you have polycystic ovarian syndrome or other reasons for anovulation. Get an amh level to check for your ovarian reserve. After testing, treatment will be advised depending on the findings.
Yes, they can be. Many conditions cause infrequent periods - commonly polycystic ovarian sydrome (pcos), also underactive thyroid, excess prolactin hormone, aging of the ovary (diminished ovarian reserve), or low hormone levels (hypogonadism) from exercise, eating disorders, etc. These conditions prevent you from ovulating regularly and affect your fertility. See a reproductive endocrinologist for tests / treatment.
Yes. Infrequent period also called oligomenorrhea. It is one of the reason of infertility. When a woman with oligomenorrhea, she does not ovulate regularly. You need to see a doctor to find out what is the underline courses.