Thalassemia is a group of inherited (passed from parents to children) blood disorders that can cause mild to severe anemia (lack of blood).
For complete answers, please see Thalassemia.

The womb or uterus is sandwiched between the bladder and the large intestine (please see diagram in female reproductive system). It can be "retroverted" (i.e. tilted backward towards the back) or "anteverted" (i.e. tilted forward towards the bladder). Neither uterine position would, in and of itself, interfere with fertility.
Most women have a slightly anteverted uterus; about one in four or five women have a retroverted uterus. However, some women may have a retroverted uterus because of endometriosis or pelvic inflammatory disease. In both cases, scar tissues pulled the uterus backward and reduce the mobility of the womb. This may cause pain during sexual intercourse and could interfere with the normal movement of the egg through the fallopian tubes, thus decreasing the chance of getting pregnant by preventing the egg from reaching the sperm

Triple blood test is a test of a set of 3 substances (alpha-fetoprotein, HCG and Oestriol) in the blood of the pregnant mother. It is usually done around the early stage of second trimester (about 14 to 18 weeks of pregnancy). It is a screening and not a diagnostic test. In other words, a positive result does not mean that the baby definitely has Down's syndrome; rather that further test such as amniocentesis is necessary to reach a conclusive diagnosis. A negative test does not mean that the baby is perfectly healthy
Click here to read more about Down's syndrome.

"Tie the tubes" or tubal ligation is a procedure in which the female is sterilized. It is an operation that blocks the fallopian tubes; this means the egg can no longer be fertilized by the sperm through sexual intercourse.
Except in rare instances, tubal ligation is 99.9% effective. It fails if the tubes that have been cut join up later on. Patient can get pregnant immediately or several years after a failed ligation. In this situation, there is increased chance of ectopic pregnancy.
The procedure is meant to be permanent, although it can be reversed by means of microscopic surgery. There is no guarantee of success.
There are usually no long-term side effects. Occasionally, patients may have heavier or irregular menstruation. There is no evidence that having it affects the sexual drive.

You can still get pregnant with only one fallopian tube as long as your ovaries still ovulate.
Normally, the ovary releases a single egg each month. The egg meets the sperm in the fallopian tube, where it is fertilized. The fertilized egg then continues its journey to the uterus and gets implanted. Only one fallopian tube is required for this to happen.
The egg released from the ovary usually enters the fallopian tube adjacent to that ovary. Although medical evidence suggests that an egg released from one ovary can be transported through the fallopian tube of the opposite side, this is not common.
As you have only one fallopian tube left and it may be partially blocked, your fertility may be reduced. There is also increased risk of tubal pregnancy.