Appliances burning out

No. Starting the truck draws from the batteries, there is no "surge." But it sounds like you have a bad inverter. It has nothing to do with the truck starting or not.

 

A.C. power by nature is "pure sin wave" (the power from the outlet at your house), A.C. power from an inverter is "modified sin wave".

In theory they're pretty much the same, but your devices can tell the difference and prefers the "pure sin wave".

There are "pure sin wave" inverters, but they are not cheap.

 

Yes.
You need to get a pure sin inverter.

 

Everything I plug into my inverter uses a power adapter (the awkward thing on the power cord that converts ac to dc power) so I've been lucky enough to only have to replace power adapters.

But yes, your stuff will keep burning up.

 

I second getting a pure sine wave inverter. Everything works much better with one. Some gadget I have would not run at all on my old modified sine wave inverter.

 

Look guys I've explained this once before, when you use cheap crap inverters, the power supplies to a lot of things can not function properly and will stop working. The power supplies for laptop chargers and gaming boxes are what is called switching power supplies and some of them are so cheap they use the line frequency to set the internal switching frequencies to produce the voltage that is needed by the item you are using.

When they get hot, they are working to adjust themselves to the noise and dirty power that they encounter with a cheap crappy inverter.

Same with the OP's microwave, it is in distress mode because of the line noise and crap that it can't filter out.

So before you try to "filter" the noise and garbage out, go get yourself a good inverter, preferably a pure sine wave and save your stuff.