In the US you can buy microwaves, fridges, etc., at almost any "big box" store, and we usually identify them by their corporate name: K Mart, Walmart, Central Radio, for example. The generic term "appliance store" works if you're looking for one.
The really easy one first - definitely not electronical shop. I don't think you'll find a dictionary definition for electronical.
The easy one next - not electronic shop. That suggests that the shop itself is electronic, not the goods it sells. A shop that sells electronic goods might be an electronics shop.
That leaves an appliance shop. Unfortunately I don't know what kind of appliances it sells - they could be surgical appliances
Now, what on earth would I call the place I would go to buy microwaves, etc.
In real life, I call it by the name above the door, whether that happens to be one of the big national chains or the local Sam's Yer Man.
If I have to generalise, I would call it an electrical appliance shop or store.
I have heard the term white goods store - these things are mostly white - but it's not something that would come naturally to me.
White goods for kitchen/household appliances (and to a much lesser extent, black goods for the...ummm....living room ones) is very commonly used, especially in trade and marketing context.
Electronics would not, normally, cover the white goods. It would cover IT equipment.
Electricals is used quite often (online retailers are often called something electricals and covers both small appliances (eg hair-driers, toasters, fans) white goods (washing machines, fridges, tumble driers, dishwashers, microwaves) and audio/video and possibly gaming equipment, but probably not strictly IT goods (PCs, printers etc).
A google suggests it's mainly a UK usage, as out of 4 million mentions, over 3 were from UK sites.
However, electricals store sounds very strange. It doesn't seem to collocate with store very well.