When you are plugged into external AC power, your AC outlets work just like at home. That's true when the generator is running and connected. The inverter will perform a similar function for small loads; probably not a blender.
The battery system is similar to what is in a car or truck. The batteries should be charged whenever the solar is active, when you are plugged into external AC power or when the generator is in use.
You should ask the folks you bought the trailer from to give you a basic rundown on how the electrical systems work.
So....yes any home blender should work fine as long as you are connected to external power or the generator is in use. The inverter is iffy and depends on the capacity of the inverter and the wattage draw of the blender.