EB is endometrial (lining of uterus) biopsy- can be done without anaesthesia - fine cannulas are available these days. It is useful in dating the endometrium. However, for establishing progesterone deficiency I would advise serum progesterone on day 21 in 3 consecutive cycles.
HSG is hysterosalpingogram - a special X-Ray test done by injecting a radio-opaque dye into uterus (without anaesthesia) which helps in ruling out any abnormality in uterine cavity (e.g small submucous fibroid, or adhesions etc.) A submucous fibroid can result in abortion. It is a test usually done to establish patency of tubes. I would advice a hysteroscopy for ruling out abnormalities in uterine cavity that can result in abortion.
ACA is anticardiolipin antibody and LA is lupus anticoagulant. These tests are advisable, because, if positive for the test you need to be treated for it. People who test positive for these tests do have a risk of abortion and other pregnancy complications. I do not know what the other abbreviations are. Best is to ask your doctor- one should never hesitate in asking question. No doctor would refuse to explain.