Q:

Understanding my electrical panel

I just purchased this breaker box from Home Depot.  I'll be installing it in my RV.  Current will be supplied by a 12VDC to 120VAC, 3000W inverter.  I'll be using Single-Pole Type BR breakers.
Here's a picture of the box:

My current understanding is that I must install a grounding bar to the box.  This is my current understanding of how to connect the breaker to the main supply.:

Here is my understanding of how I would wire in new circuits:

Does this look right?  I would really appreciate your help -- I've been beating myself over the head about this.

A:

Do Not put BR breakers in a Murray/Siemens panel.
Breakers must match the panels.  Those will not fit properly. 
You can either use Murray (Siemens) breakers in this panel... 
... or take it back and get an Eaton BR 2-space panel of same type. 
If you are married to this panel and have an Eaton gift card to use up, then get Eaton CL breakers, which are specifically made by Eaton for Siemens panels, and have been UL-listed (classified) for that purpose. 
But you're on the right track
Just work it one step at a time. Your first drawing shows a correct hookup for a panel, with the accessory grounding bar you added, and with a special jumper between the two "poles" since you are using this as a 120V panel. 
Now, there's one gotcha here.  As drawn, it has 2 wires on 1 lug.  That's not allowed.  Split the incoming hot onto two pigtails at a wire nut.  
As for the branch circuits, you are connecting them correctly, in the manner which is "bog standard".  
The neutral-ground bond
Now, this is a bit complicated.  Neutral and ground are separate.  Ground is only a safety shield, and neutral is the normal current return.   However, what stops neutral from floating at dozens or thousands of volts from ground?  The answer is a neutral-ground bond in exactly one place.  It must not be in 2 places, or it will destroy the grounding system's ability to protect you. 
When you are on hotel power, (i.e. off a house), the one neutral-ground bond is in the house's main panel. 
When you are on local power, the one neutral-ground bond needs to be somewhere.    Most consumer-tier sources of electricity, e.g. a portable generator or inverter, have a built-in neutral-ground bond.  Check it; if so that means your panel must have another. 
Switching between inverter and hotel power
When you are docked, you want to be able to run on terrestrial utility power.  The "hard way" is with a transfer switch, and a service-panel/transfer switch combo is the cheapest way to do that, but still expensive because you need to switch neutral.  You can either use CDN$300 Canadian-style generator interlock panels, which have a 3-pole interlocked breaker that also switches neutral; or since your service is 120V, you can use a normal 2-pole panel with transfer switch kit, and make neutral one of the two poles. This makes the interlocked panel cheaper, but the breakers more expensive. For 2 circuits, an 8-space Square D "QO" panel will git-r-done in a compact package for about USA$130 - cheaper than the Canadian panels but still a lot. 
However, the easiest way by far for a 30A supply is simply to use a loopback cord.  
You bring the inverter's output to a junction box, and the panel's input to a junction box right next to it.  The inverter's output goes to a 120V/30A receptacle, either a NEMA L5-30, or a TT30.  The panel's input just has a 1 foot long cord coming out of it. Normally it's plugged into the inverter output.  
For shore power, you unplug from that socket, and plug into an extension cord to the house.  
The neutral switching gets magically handled by the plug/socket! 

