Question : Problem: will a 1gbit switch speed be downgraded if a 100mbit switch is connected to it?

I have a 100mbit switch connected to a 1gbit switch but will our whole network operate at 100mbit because of this one switch?  

Is there a 1Gbit bus line that all 16 ports share or each port is independent and the bus line bandwidth runs at 16gbits+?

Answer : Problem: will a 1gbit switch speed be downgraded if a 100mbit switch is connected to it?

By design, each port in the switch is independent.

So, the answer is no.  Only the one link will be 100Mb.