Does heavy discharge mean I have an infection?

No. Vaginal discharge in pregnancy is common from all the hormonal changes. This does not necessarily mean that you have an infection. On the other hand, vaginal discharge could be caused by an infection and you should be test. The most common infections are bacterial vaginosis and yeast which are not sexually transmitted. Stis like gonorrhea, chlamydia and trichomoniasis should be ruled out.
Yes. Heavy vaginal doesn't necessarily mean infection. It should be check by your gyn by a wet mount prep (examination of the discharge under the microscope), and cultured as well. Frequently the diagnosis can be established by microscopic examination alone. The examiner can see "clue" cells in an infection with bv, yeast hyphae in yeast vaginitis or motile trichmonads in trichomonal vulvovaginitis.
No. If your discharge doesn't itch, burn or smell badly, it's probably physiologic and related to the amount of blood flow in the vagina and the mucous from the cervix.
No. No not necessarily. Have your doctor evaluate you. The cervix is a gland that produces lots of mucus. This mucus has chemicals and compounds in it that prevent infections from affecting the pregnancy. The discharge pushes out bacteria, etc in a unidirectional cleaning mechanism.