I would like to replace the arduino nano with a 40Mhz transducer
The wiring I am unsure about. I do not know if GND needs to be tied from the opamp supply and the transducer?
No you don't.The scope has its probe in a not calibrated state.
a) The opamp claims 1Mhz bandwidth
No it doesn't, not the way you're thinking. Read more carefully. It says 1 MHz unity gain bandwidth, also known as the gain-bandwidth product.In order to get the actual bandwidth of your configuration, you need to divide the GBP by your gain.In this case, 1 MHz / 10,000 gain = 100 Hz bandwidth.You either need to cascade your op amp stages to get the bandwidth you want (http://www.eevblog.com/2014/01/25/eevblog-572-cascading-opamps-for-increased-bandwidth/), or get a much higher bandwidth op amp.
I need to cascade 6 1Mhz opamps
Get rid of the coupling cap.