How do I test to make sure my panel is grounded correctly and all the bonding is correct?
A continuity test should be sufficient to determine that the grounding wires are connected. Edit- To check for continuity with a multimeter, turn the dial to the a symbol that looks like, ►|. Make sure the probes are in the correct places. Some multimeters have three sockets for two probe wires... if that's the kind of multimeter that you have you need to put one probe in the socket marked ohms (Ω). Then attach or touch the probes to whatever you are checking (for continuity) to find out if they are connected. Some multimeter models make a ringing noise, while other models just display a quick burst of numbers which settle down to zero when the meter senses that the probes are connected (electrically).

But beyond that you should check out the article, how to achieve grounding in poor soil. I'm not suggesting that you have poor soil, but this article illustrates how to check it (with a ground resistance testing instrument) and how to treat poor soil if necessary, and points out some other info about grounding.