Heavy flow of bleeding like having a period possible during first four weeks of pregnancy?

Yes. "decidual bleeding" can be lumped together with "implantation bleeding" and we can call them both "first trimester bleeding". I'd estimate 20-30% of pregnant women have some type of first trimester bleeding, and many go on to have normal pregnancies. An ultrasound is the only way to know that things are ok in there and to rule out an ectopic. An hpt will still be positive if you are miscarrying.