What kind of engineers fix things?

They're more often called technicians if they're in the area of fixing faulty devices. You'll often find the technicians come up with an ideal solution to remedy a poorly engineered product. Companies won't pay the salary an engineer requires when they can have a lower qualified and less expensive person to do the same job.

It depends on the problem. Some times it is a maintenance engineer and other times it is just an engineer who has been assigned the job of fixing a problem.

I my career I have had all of those assignments. Designing things, building things, starting things up, operating things and fixing things.

"What kind of field engineer finds a problem of something that's broken and finds the solution to fixing it?"

no kind

the solution to fixing something thats broken is to replace it.
Its only occasionally do you have to come up with a temporary fix until you get the replacement

Thing you have to remember is that whatever it is has been designed to work with that part , NOT some other part or a work-around
Another part or work-around could lead to premature failure of another part or a complete failure of the unit

(and "engineer" is the most overused title
to call somebody a "feild engineer" implies they are "engineers" who happen to work in the field - they are far from this

(story from a computer mag editor who wrote it in his editorial
- He called out a so called "field engineer" to fix a colour laser printer costing thousands
the "engineer" couldnt work out how to get into the printer to fix it - so he took out a drill
The editor only just managed to stop him drilling to get the covers off the printer)

DEEZ nuts

Electrical and Technical.

MOSTLY IS DONE BY A SKILLFUL TECHNICIAN IN REPAIR AND TROUBLE SHOOTING FIELD. MOST ENGINEER DOES NOT KNOW HOW TO DO A REPAIR OR TROUBLE SHOOT TO LOCATE THE FAILURE.

The same kind of engineer that builds it, with additional experience/training in forensic examination to detect problems.

Field engineers
Quality Control Engineers

Field engineer is actually a great adjective. Frequently don't need an engineering degree to be a field engineer.

The same as the one who designed it, except thay have focused theri PErSONAAL interest into ficing rather than designing