Before the Mazda I had a yaris with ABS brakes therefore I have no idea how braking a car with no ABS would sound. But I'm really finding it strange that with the minimal brake, the car makes a heavy screech as if I were braking from a 100mph race where in fact I am going in a miserable 35 mph.. Do you think i need to change the brake shoes?

Yes.

Hey there. It all depends on what kind of schreecing noise it is. Does it sound like a grinding noise or just a light scraping noise. The front inner pads on my 1.8se has a metal pin on them. When the pads are usually worn this pin will touch the discs and make a screeching noise indicating that the pads needs to be replaced. It can also be that the pads is manufactured from a harder compound. My current front disc pads are made from a hard compound and when I only brake softly it will make a terrible grinding noise. Try to fit pads made from a softer compound.

Hope this helps you.