You don't have a period while pregnant. The two are impossible to have at the same time. This is because during a period you shed the uterine lining that is built up to support a fertilized egg. If it remains unfertilized this lining is shed. If it's fertilized, the egg embeds into the lining and starts to grow. If you shed this while pregnant, you'd miscarry. As the others have said, urine and bleeding are in the same general area and often while you use the bathroom the two more or less combine. Only way to know if you're pregnant is to take a pregnancy test with first morning urine.
Every time I'm on my period my 'pee' has blood in it. It doesn't have to be particularly heavy for me at least. They just come from the same area and you keep bleeding even while urinating.
I'm not sure about pregnancy. The only way you can be sure is pregnancy tests or doctors.
It could just be that your period is heavy, ive had this happen many times if ive had a heavy period, especially during the first day or two of my period starting.