For example, can I say:
Have you got checked the fuses by electrician?
For example, can I say:
Have you got checked the fuses by electrician?
That example sentence is wrong. You could say "Have you had the fuses checked by the electrician?" or "Have the fuses been checked...?"
In informal speech I have heard something like "Have you got beaten at football again?" but in formal language "been" would replace "got".
"Have you got it solved?" works as a question to a maths student who has been struggling with a problem. So on the basis that a single example shows that something is possible, the answer to your question is "yes you can", but I had to think hard to come up with that example. It is not a common construction and not for formal use..