Hi rvan,
1. HP produce a 12v to 15 thro to 19v selectable power adapter for your laptop computer. This is the preferred method as if you use a 1500w inverter, it would be very inefficient use of your battery capacity.
2. Depends on inverter manufacturer, however it will still draw a small amount of standing current if it is not switched off.
3. Depends on the size of inverter and battery, but with a 1500w inverter generally you would only be able to run one heavy current appliance at a time.
4. Electric blankets are 100% efficient whether 110v or 12v. The issue comes down to other losses in the distribution system of getting power to the blanket. If you use the inverter to run your 110V electric blanket, typically 100w or less load, then there are considerable losses in running the inverter. Much better to run the electric blanket off 12v.
5. Lights.. use LED lights, the current drain on these for the same light output as an incandescent light is 10% and 20% lower than a fluorescent lamp.
Water pump uses about 3 amps when running. As you normally are not running the pump for more than a few seconds at a time, the pump is not a signficant user of battery energy.
6. Charging small appliances... use a small inverter, say 60 to 100watts for these as it is most inefficient to use a 1500w inverter for this use. Run fans off 12v.
7. Inverter to run microwave and induction hob. Inverters are rated for a completely resistive load. some do have a short term rating which is higher than the continuous rating. Microwaves and inductive hobs have very high inrush currents. This requires an inverter rated at least 1.5 to 2 times larger than the appliance rating.
8. Roof mounted solar panels may affect fuel consumption but not very significantly... say 1%. Compare the area of the front of the vehicle to the forward face of the solar panel!! Ches makes good valid points, but it depends on where you are travelling to. If you are not going above about 40 degrees North then mounting solar panels permanently horizontal is OK. Allow for about 10% increase in size to correct for the area loss due to not facing directly to the sun. Do you want to constantly be moving the panel to get maximum charge?!!! If you mount the panel on the roof then ensure that it is spaced about 1 inch above the roof to allow airflow under it, as solar panels lose their conversion efficiency when hot.
My advise on the high power devices is dont fit them. Cedarsanctum has made very valid points here.
Batteries and charging... A conventional liquid lead acid deep cycle battery can only be charged to about 75 to 80% from the engine alternator or solar panel with a conventional regulator. As Cedarsanctum says, they should not be discharged below 50%. That means that your battery only has a useful energy storage of 25 to 30% !!! This is why so many installations fail early. To fix this problem, use an agm or gel battery and a solar regulator which has MPPT capability. (Maximum power point transfer) see
http://en.wikipedia.org/wiki/Maximum_power_point_tracker
This will charge a gel battery to 100% and the gel battery can be discharged to 30% giving you a useful capacity of 70%!!
Also use a single 12v battery with the capacity required instead of two or more batteries in parrellel. Batteries in parrellel will not fully charge equally as the internal resistance of each battery may be different. particularly over time. Batteries in series are OK as the same amount of current will flow through both. ie 2 x 6v. However they tend to be dearer than a single battey of the same total Amphour capacity.
One last point. Wiring... Ensure that the wire size to each appliance is adequate for the job. Use the rule of thumb that the voltage drop from the battery to the appliance when running should not exceed 3%. At 12v this equates to 0.36Volts.
Whew!!! I think that is enough for today.
Hope this helps
Cheers Ross