Hate to disagree with anyone but placenta praevia grade 4 is serious. I had it. And at Kings I was told it was extremely unlikely that a grade 4 placenta praevia would 'move' enough for it not to be an issue at term - I was diagnosed at 14 weeks if I remember correctly.
Most placenta praevias aren't a problem at term because they are much higher up to start with - ie Placenta Praevia grade 1 means just that some of the placenta is in the lower segment of the uterus, and that is a very different thing to the placenta lying directly over the os. The baby will be fine at this stage because it is your blood - not from the baby. Have you been told to stay as inactive as possible? ie no brisk walks, no exercise, and no penetrative sex? Sex is a no-no with pp - esp grade 4 and does cause bleeding. I was lucky, apart from bleeding after sex in the early days, I didn't have a 'proper' bleed until 30 weeks. I had a normal, very healthy pregnancy but was in hospital from 32 weeks until nearly 38 weeks when my son was born in a relatively uncomplicated c-section under spinal block.
For you it is early days, but you should get to talk to a consultant about the position of your placenta, your bleeding episodes and get some advice. As I said, my advice was that the placenta was very likely to remain low-lying (and it never moved off the os in my case) but you may be told something different.