New CDL A License Looking At Truck Companies

I was looking at truck companies. I got my license through a truck company in their training. They pay for their school if I stay for one year, or I pay it if I leave.

If I leave for another company, do I need to ask for a school certificate or anything to prove I had training and time on the road?

Are there companies that pay .60-.70 cpm for 3-6 months of driving?

I want to do heavy oversized loads. How do I get into that? I'm driving for spread axle flatbed now, but looking to change companies for better pay and other reasons to get more experience time

You won't find better pay by jumping ship now. You will be setting yourself up for failure by leaving your current company with so little experience. It's highly unlikely that you will find that kind of pay with less than a year of experience. Your best option is to stick with your current company for at least a year, two years even better, then apply with companies that specialize in heavy haul.