1) As far as the wood is concerned its a good idea once you get your fire started to set the next couple of pieces you plan to burn on the hearth. This allows the wood to expand a bit and allows any surface moisure to dissipate. Also, try starting the softer, lighter wood first, then trow on the heavier hard woods, such as eucalyptus. Eucalyptus has really coarse and splittery grain and is reddish in color. Remember that with harder woods such as eucalyptus, it needs to be stoked to keep it burning consistently through. Starter logs or Fat Wood (starter sticks) are helpful if your fireplace doesn't have natural gas piped in to help start the fire.
2) When covering up firewood outside with a tarp only do so if wet weather is on the way or if you live in a coastal location which has moist mornings or evenings (fog). Completely covering firewood for extended periods of time may result in mildew and a faster breakdown of the cellulose material that wood is made of, as covering it traps moisture. let the wood breath and it will burn well when started. There are covers sold that just cover the top of the stack and then some. These are recommended for the Southern California climate such as ours.