An inverter converts DC power to AC power. AC power is what comes out of the outlet (at 50 Hz or 50 cycles per second in Laos and France.) All laptops have rectifiers that convert outlet power from AC to DC.
Inverters may help the power quality because they use diodes which may help regulate the voltage and reduce harmonics (which are caused by having motors and things like fluorescent light fixtures and computers on the same system as the outlet you're plugging into). The study of harmonics, how they're created, and how to mitigate them is a giant field. Harmonics are most likely what would cause strange electrical behaviors. They would not likely burn up any equipment though. I can't comment on the strange behavior unless I know what it is.
Stabilizers regulate voltage (or the peaks of the AC cylce). It is very common in poorer countries to have lots of problems with voltage regulation.
It is difficult to find information on the power quality in Laos. For example, here is a chart listing the voltage tolerance (aka voltage regulation) of many countries where Laos isn't even listed. http://www.ipqdf.com/pq-info/international-frequency-and-voltage-levels/ This tells me that it is likely the quality is poor because if you aren't measuring something, you can't fix it. This is a report that states in the introduction that little information is know about power quality in southeast Asia. http://www.copper.org.sg/sites/default/files/publications/files/UNEP2012-PQ_0.pdf It also includes a survey from Thailand, Vietnam and Indonesia of power quality issues. The general gist if the report indicates very poor power quality in this region.
Your main concern for burning up any equipment would be voltage surges, or cases where the voltage spikes too high or cases where it stays at higher than 230 for too long of a time. Spikes are generated for a number of reasons and are more likely in poorer countries that built there infrastructure with less regulations than more developed countries. For example, an outage in one area could cause a spike in another, overhead or poorly insulated power lines touch together, protection devices fail, etc. For this, it is a good idea to have a surge protector (aka, voltage regulator, stabilizer) as electronic equipment like your laptop is more sensitive to these surges than other devices and could get "fried" by these surges.
The likely hood of this increases the closer you are to the power plant and/or the power transformer serving your location.
None of the protection devices protect from network breakdown and network breakdown is not a threat to the laptop. Although, since laptops have batteries in them, you have an automatic backup power source so you don't have to worry about losing data, just time once your batteries run out.
Plugging into a 110v source with a 220v device is not a risk. Most laptops are built for international voltages and are rated for 230v. You should never plug 110v device into a 220v source without a voltage converter (aka transformer). Overload and destruction of the device is guaranteed.
Recommended maintenance for the health of the machine as far as electricity is concerned would be to use a surge protector especially in areas with poor power quality like Laos, turn the machine off and let it cool down if it gets too hot (to the point where touching the batter compartment is uncomfortable), and "exercise" the battery (let it run on battery power every so often - every 3 days or so - down to 50% battery or even the low battery warning).
I hope all of this information cleared up a few things and didn't just make them more confusing!