I have some polyester thread on small spools. Would I be able to use it on my bobbins with cotton threads? Is this not a good idea?

It's preference. I prefer all cotton thread.

I would use either poly or cotton, I would not mix them together.

If they are old , do a thread break test. Test to see how easily it breaks in comparison to fresh thread . If its all OK , go ahead and use it , I mix my threads ... ALOT!

they say to use the same type of tread and also the same weight.

i use whatever type i have mix/match/whatever . . . as long as it is of good quality, for piecing. i am more particular when quilting. using "cheap" thread is NEVER worth it.

if you press with a hot iron, you can melt polyester thread and lose your stitches!

I mix poly with cotton and different weights all the time. My bobbin thread is almost always lighter than the needle thread, but in the case of decorative work, you'd use a heavy thread in the bobbin and a fine/invisible thread in the needle. You just have to adjust the tensions properly for each thread. Set the tension on the bobbin for the bobbin thread, then adjust the tension on the needle thread to balance with the bobbin thread. It will be second nature before you know it. :)

Every time I buy a vintage sewing machine, at least one of the cabinet drawers is usually filled with old spools of thread. I keep the wooden spools and the Coats & Clark cotton and poly/cotton and other "good" threads and I throw away the styrofoam spools and brands that don't pass the break test. The Coats & Clark from the 70's and earlier usually chugs right along. :)