I'll just add my 2 bits to all the great comments already given. It's a new doctor, and every one has a different way of doing things. All those tests seem scary, but some doctors prefer them. But, the question is, do you? Your pregnancy sounds normal, and nature will have to take its course either way, but the best thing you can do is to enjoy your pregnancy, eat right, exercise, and try to stay positive. If you aren't sure about they whys for tests, get answers. If you don't like the answers or don't agree, find another doctor or midwife. It's a hassle, but the hassle is better than having a stressed out pregnancy, constantly worrying about the outcome of all these tests, when 1)it's not likely you have any problem, and 2)even if there is a problem, there isn't much, if anything, that could be done about it (except to make sure you have plenty of protein and iron in your diet). You stay healthy, the baby will continue to grow, and everything will be the way it's meant to be, and you can be happy with your babies, both present and growing.
Remember, too, you don't have to have all, or even any, of the tests/procedures the doctor wants you have. It is perfectly okay not to have any of them! Do what is best for you and your sanity, and everything will be okay.
I didn't like the constant attempts at medical intervention during my pregnancies, nor the attempted guilt trips if I wouldn't do the procedures they wanted, so I went to a midwife who had a similar philosophy and comfort level with letting nature take its course, and a knowledge of natural, non-intervention ways of doing things, focusing on diet, and overall health, and the knowledge of what to look for and when and how to prevent problems, and of when medical intervention is necessary.
So, I had only minimal tests for 3 of my 6 pregnancies (2 of them were miscarriages, which nothing could have helped) -- an initial blood prick to check my iron levels and adjust my diet accordingly, and (for the last one) that GBS test at the end to make sure I didn't have too many of the strep bacteria at the birth. That was it -- no ultrasounds or vials of blood or anything else. We had regular prenatals to check on the growth of the baby and my overall health and diet and weight gain, and diet adjustments if necessary, and that was it. They were very peaceful pregnancies, and they all turned out well.
Everyone is different, and have different comfort levels with medical intervention. Do what you feel most comfortable with. Use a doctor or midwife that you are comfortable with, and whose practices you are comfortable with. Above all, stick to what you are comfortable with, and trust your own instincts.
Congratulations, and good luck!